Algebraic Curves over a Finite Field:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton
Princeton University Press
2013
|
| Schriftenreihe: | Princeton series in applied mathematics
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Chapter 9. Zeta functions and curves with many rational points Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi |
| Beschreibung: | 1 Online-Ressource (717 pages) |
| ISBN: | 1400847419 9781400847419 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV043068802 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 151126s2013 |||| o||u| ||||||eng d | ||
| 020 | |a 1400847419 |9 1-4008-4741-9 | ||
| 020 | |a 9781400847419 |9 978-1-4008-4741-9 | ||
| 035 | |a (OCoLC)889240929 | ||
| 035 | |a (DE-599)BVBBV043068802 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-1046 |a DE-1047 | ||
| 082 | 0 | |a 516.352 | |
| 100 | 1 | |a Hirschfeld, J. W. P. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Algebraic Curves over a Finite Field |
| 264 | 1 | |a Princeton |b Princeton University Press |c 2013 | |
| 300 | |a 1 Online-Ressource (717 pages) | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 490 | 0 | |a Princeton series in applied mathematics | |
| 500 | |a Chapter 9. Zeta functions and curves with many rational points | ||
| 500 | |a Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem | ||
| 500 | |a 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations | ||
| 500 | |a 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes | ||
| 500 | |a Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem | ||
| 500 | |a 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes | ||
| 500 | |a This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi | ||
| 650 | 7 | |a MATHEMATICS / Geometry / General |2 bisacsh | |
| 650 | 7 | |a Curves, Algebraic |2 fast | |
| 650 | 7 | |a Finite fields (Algebra) |2 fast | |
| 650 | 4 | |a Curves, Algebraic | |
| 650 | 4 | |a Finite fields (Algebra) | |
| 650 | 0 | 7 | |a Algebraische Kurve |0 (DE-588)4001165-3 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Galois-Feld |0 (DE-588)4155896-0 |2 gnd |9 rswk-swf |
| 655 | 7 | |8 1\p |0 (DE-588)4006432-3 |a Bibliografie |2 gnd-content | |
| 689 | 0 | 0 | |a Algebraische Kurve |0 (DE-588)4001165-3 |D s |
| 689 | 0 | 1 | |a Galois-Feld |0 (DE-588)4155896-0 |D s |
| 689 | 0 | |8 2\p |5 DE-604 | |
| 700 | 1 | |a Korchmáros, G. |e Sonstige |4 oth | |
| 700 | 1 | |a Torres, F. |e Sonstige |4 oth | |
| 856 | 4 | 0 | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476 |x Aggregator |3 Volltext |
| 912 | |a ZDB-4-EBA | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-028492994 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 883 | 1 | |8 2\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476 |l FAW01 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
| 966 | e | |u http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476 |l FAW02 |p ZDB-4-EBA |q FAW_PDA_EBA |x Aggregator |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804175450141884416 |
|---|---|
| any_adam_object | |
| author | Hirschfeld, J. W. P. |
| author_facet | Hirschfeld, J. W. P. |
| author_role | aut |
| author_sort | Hirschfeld, J. W. P. |
| author_variant | j w p h jwp jwph |
| building | Verbundindex |
| bvnumber | BV043068802 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)889240929 (DE-599)BVBBV043068802 |
| dewey-full | 516.352 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.352 |
| dewey-search | 516.352 |
| dewey-sort | 3516.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>05846nmm a2200601zc 4500</leader><controlfield tag="001">BV043068802</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">151126s2013 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1400847419</subfield><subfield code="9">1-4008-4741-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781400847419</subfield><subfield code="9">978-1-4008-4741-9</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)889240929</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV043068802</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-1046</subfield><subfield code="a">DE-1047</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">516.352</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Hirschfeld, J. W. P.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Algebraic Curves over a Finite Field</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Princeton</subfield><subfield code="b">Princeton University Press</subfield><subfield code="c">2013</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 Online-Ressource (717 pages)</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="0" ind2=" "><subfield code="a">Princeton series in applied mathematics</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Chapter 9. Zeta functions and curves with many rational points</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS / Geometry / General</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Curves, Algebraic</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finite fields (Algebra)</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Curves, Algebraic</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finite fields (Algebra)</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Algebraische Kurve</subfield><subfield code="0">(DE-588)4001165-3</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Galois-Feld</subfield><subfield code="0">(DE-588)4155896-0</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="8">1\p</subfield><subfield code="0">(DE-588)4006432-3</subfield><subfield code="a">Bibliografie</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Algebraische Kurve</subfield><subfield code="0">(DE-588)4001165-3</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Galois-Feld</subfield><subfield code="0">(DE-588)4155896-0</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">2\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Korchmáros, G.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Torres, F.</subfield><subfield code="e">Sonstige</subfield><subfield code="4">oth</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-028492994</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">2\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476</subfield><subfield code="l">FAW01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476</subfield><subfield code="l">FAW02</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FAW_PDA_EBA</subfield><subfield code="x">Aggregator</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| genre | 1\p (DE-588)4006432-3 Bibliografie gnd-content |
| genre_facet | Bibliografie |
| id | DE-604.BV043068802 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:29Z |
| institution | BVB |
| isbn | 1400847419 9781400847419 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028492994 |
| oclc_num | 889240929 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (717 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Princeton University Press |
| record_format | marc |
| series2 | Princeton series in applied mathematics |
| spelling | Hirschfeld, J. W. P. Verfasser aut Algebraic Curves over a Finite Field Princeton Princeton University Press 2013 1 Online-Ressource (717 pages) txt rdacontent c rdamedia cr rdacarrier Princeton series in applied mathematics Chapter 9. Zeta functions and curves with many rational points Cover; Title; Copyright; Dedication; Contents; Preface; PART 1. GENERAL THEORY OF CURVES; Chapter 1. Fundamental ideas; 1.1 Basic definitions; 1.2 Polynomials; 1.3 Affine plane curves; 1.4 Projective plane curves; 1.5 The Hessian curve; 1.6 Projective varieties in higher-dimensional spaces; 1.7 Exercises; 1.8 Notes; Chapter 2. Elimination theory; 2.1 Elimination of one unknown; 2.2 The discriminant; 2.3 Elimination in a system in two unknowns; 2.4 Exercises; 2.5 Notes; Chapter 3. Singular points and intersections; 3.1 The intersection number of two curves; 3.2 Bézout's Theorem 3.3 Rational and birational transformations3.4 Quadratic transformations; 3.5 Resolution of singularities; 3.6 Exercises; 3.7 Notes; Chapter 4. Branches and parametrisation; 4.1 Formal power series; 4.2 Branch representations; 4.3 Branches of plane algebraic curves; 4.4 Local quadratic transformations; 4.5 Noether's Theorem; 4.6 Analytic branches; 4.7 Exercises; 4.8 Notes; Chapter 5. The function field of a curve; 5.1 Generic points; 5.2 Rational transformations; 5.3 Places; 5.4 Zeros and poles; 5.5 Separability and inseparability; 5.6 Frobenius rational transformations 5.7 Derivations and differentials5.8 The genus of a curve; 5.9 Residues of differential forms; 5.10 Higher derivatives in positive characteristic; 5.11 The dual and bidual of a curve; 5.12 Exercises; 5.13 Notes; Chapter 6. Linear series and the Riemann-Roch Theorem; 6.1 Divisors and linear series; 6.2 Linear systems of curves; 6.3 Special and non-special linear series; 6.4 Reformulation of the Riemann-Roch Theorem; 6.5 Some consequences of the Riemann-Roch Theorem; 6.6 The Weierstrass Gap Theorem; 6.7 The structure of the divisor class group; 6.8 Exercises; 6.9 Notes Chapter 7. Algebraic curves in higher-dimensional spaces7.1 Basic definitions and properties; 7.2 Rational transformations; 7.3 Hurwitz's Theorem; 7.4 Linear series composed of an involution; 7.5 The canonical curve; 7.6 Osculating hyperplanes and ramification divisors; 7.7 Non-classical curves and linear systems of lines; 7.8 Non-classical curves and linear systems of conics; 7.9 Dual curves of space curves; 7.10 Complete linear series of small order; 7.11 Examples of curves; 7.12 The Linear General Position Principle; 7.13 Castelnuovo's Bound; 7.14 A generalisation of Clifford's Theorem 7.15 The Uniform Position Principle7.16 Valuation rings; 7.17 Curves as algebraic varieties of dimension one; 7.18 Exercises; 7.19 Notes; PART 2. CURVES OVER A FINITE FIELD; Chapter 8. Rational points and places over a finite field; 8.1 Plane curves defined over a finite field; 8.2 Fq-rational branches of a curve; 8.3 Fq-rational places, divisors and linear series; 8.4 Space curves over Fq; 8.5 The Stöhr-Voloch Theorem; 8.6 Frobenius classicality with respect to lines; 8.7 Frobenius classicality with respect to conics; 8.8 The dual of a Frobenius non-classical curve; 8.9 Exercises; 8.10 Notes This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristi MATHEMATICS / Geometry / General bisacsh Curves, Algebraic fast Finite fields (Algebra) fast Curves, Algebraic Finite fields (Algebra) Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Galois-Feld (DE-588)4155896-0 gnd rswk-swf 1\p (DE-588)4006432-3 Bibliografie gnd-content Algebraische Kurve (DE-588)4001165-3 s Galois-Feld (DE-588)4155896-0 s 2\p DE-604 Korchmáros, G. Sonstige oth Torres, F. Sonstige oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hirschfeld, J. W. P. Algebraic Curves over a Finite Field MATHEMATICS / Geometry / General bisacsh Curves, Algebraic fast Finite fields (Algebra) fast Curves, Algebraic Finite fields (Algebra) Algebraische Kurve (DE-588)4001165-3 gnd Galois-Feld (DE-588)4155896-0 gnd |
| subject_GND | (DE-588)4001165-3 (DE-588)4155896-0 (DE-588)4006432-3 |
| title | Algebraic Curves over a Finite Field |
| title_auth | Algebraic Curves over a Finite Field |
| title_exact_search | Algebraic Curves over a Finite Field |
| title_full | Algebraic Curves over a Finite Field |
| title_fullStr | Algebraic Curves over a Finite Field |
| title_full_unstemmed | Algebraic Curves over a Finite Field |
| title_short | Algebraic Curves over a Finite Field |
| title_sort | algebraic curves over a finite field |
| topic | MATHEMATICS / Geometry / General bisacsh Curves, Algebraic fast Finite fields (Algebra) fast Curves, Algebraic Finite fields (Algebra) Algebraische Kurve (DE-588)4001165-3 gnd Galois-Feld (DE-588)4155896-0 gnd |
| topic_facet | MATHEMATICS / Geometry / General Curves, Algebraic Finite fields (Algebra) Algebraische Kurve Galois-Feld Bibliografie |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=816476 |
| work_keys_str_mv | AT hirschfeldjwp algebraiccurvesoverafinitefield AT korchmarosg algebraiccurvesoverafinitefield AT torresf algebraiccurvesoverafinitefield |