Geometric Modular Forms and Elliptic Curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
2011
|
| Ausgabe: | 2nd ed |
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Preface to the second edition; Preface; Contents; 1. An Algebro-Geometric Tool Box; 1.1 Sheaves; 1.1.1 Sheaves and Presheaves; 1.1.2 Sheafication; 1.1.3 Sheaf Kernel and Cokernel; 1.2 Schemes; 1.2.1 Local Ringed Spaces; 1.2.2 Schemes as Local Ringed Spaces; 1.2.3 Sheaves over Schemes; 1.2.4 Topological Properties of Schemes; 1.3 Projective Schemes; 1.3.1 Graded Rings; 1.3.2 Functor Proj; 1.3.3 Sheaves on Projective Schemes; 1.4 Categories and Functors; 1.4.1 Categories; 1.4.2 Functors; 1.4.3 Schemes as Functors; 1.4.4 Abelian Categories; 1.5 Applications of the Key-Lemma 1.5.1 Sheaf of Differential Forms on Schemes1.5.2 Fiber Products; 1.5.3 Inverse Image of Sheaves; 1.5.4 Affine Schemes; 1.5.5 Morphisms into a Projective Space; 1.6 Group Schemes; 1.6.1 Group Schemes as Functors; 1.6.2 Kernel and Cokernel; 1.6.3 Bialgebras; 1.6.4 Locally Free Groups; 1.6.5 Schematic Representations; 1.7 Cartier Duality; 1.7.1 Duality of Bialgebras; 1.7.2 Duality of Locally Free Groups; 1.8 Quotients by a Group Scheme; 1.8.1 Naive Quotients; 1.8.2 Categorical Quotients; 1.8.3 Geometric Quotients; 1.9 Morphisms; 1.9.1 Topological Definitions; 1.9.2 Diffeo-Geometric Definitions 1.9.3 Applications1.10 Cohomology of Coherent Sheaves; 1.10.1 Coherent Cohomology; 1.10.2 Summary of Known Facts; 1.10.3 Cohomological Dimension; 1.11 Descent; 1.11.1 Covering Data; 1.11.2 Descent Data; 1.11.3 Descent of Schemes; 1.12 Barsotti-Tate Groups; 1.12.1 p-Divisible Abelian Sheaf; Exercise; 1.12.2 Connected- Etale Exact Sequence; 1.12.3 Ordinary Barsotti-Tate Group; 1.13 Formal Scheme; 1.13.1 Open Subschemes as Functors; Exercises; 1.13.2 Examples of Formal Schemes; 1.13.3 Deformation Functors; 1.13.4 Connected Formal Groups; 2. Elliptic Curves; 2.1 Curves and Divisors 2.1.1 Cartier Divisors2.1.2 Serre-Grothendieck Duality; 2.1.3 Riemann-Roch Theorem; 2.1.4 Relative Riemann-Roch Theorem; 2.2 Elliptic Curves; 2.2.1 Definition; 2.2.2 Abel's Theorem; 2.2.3 Holomorphic Differentials; 2.2.4 Taylor Expansion of Differentials; 2.2.5 Weierstrass Equations of Elliptic Curves; 2.2.6 Moduli of Weierstrass Type; 2.3 Geometric Modular Forms of Level 1; 2.3.1 Functorial Definition; 2.3.2 Coarse Moduli Scheme; 2.3.3 Fields of Moduli; 2.4 Elliptic Curves over C; 2.4.1 Topological Fundamental Groups; 2.4.2 Classical Weierstrass Theory; 2.4.3 Complex Modular Forms 2.5 Elliptic Curves over p-Adic Fields2.5.1 Power Series Identities; 2.5.2 Universal Tate Curves; 2.5.3 Etale Covering of Tate Curves; 2.6 Level Structures; 2.6.1 Isogenies; 2.6.2 Level N Moduli Problems; 2.6.3 Generality of Elliptic Curves; 2.6.4 Proof of Theorem 2.6.8; Exercise; 2.6.5 Geometric Modular Forms of Level N; 2.7 L-Functions of Elliptic Curves; 2.7.1 L-Functions over Finite Fields; 2.7.2 Hasse-Weil L-Function; 2.8 Regularity; 2.8.1 Regular Rings; 2.8.2 Regular Moduli Varieties; 2.9 p-Ordinary Moduli Problems; 2.9.1 The Hasse Invariant; 2.9.2 Ordinary Moduli of p-Power Level 2.9.3 Irreducibility of p-Ordinary Moduli This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti-Tate groups (including formal Li |
| Beschreibung: | 1 Online-Ressource (468 pages) |
| ISBN: | 9789814368650 9814368652 |
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| 500 | |a Preface to the second edition; Preface; Contents; 1. An Algebro-Geometric Tool Box; 1.1 Sheaves; 1.1.1 Sheaves and Presheaves; 1.1.2 Sheafication; 1.1.3 Sheaf Kernel and Cokernel; 1.2 Schemes; 1.2.1 Local Ringed Spaces; 1.2.2 Schemes as Local Ringed Spaces; 1.2.3 Sheaves over Schemes; 1.2.4 Topological Properties of Schemes; 1.3 Projective Schemes; 1.3.1 Graded Rings; 1.3.2 Functor Proj; 1.3.3 Sheaves on Projective Schemes; 1.4 Categories and Functors; 1.4.1 Categories; 1.4.2 Functors; 1.4.3 Schemes as Functors; 1.4.4 Abelian Categories; 1.5 Applications of the Key-Lemma | ||
| 500 | |a 1.5.1 Sheaf of Differential Forms on Schemes1.5.2 Fiber Products; 1.5.3 Inverse Image of Sheaves; 1.5.4 Affine Schemes; 1.5.5 Morphisms into a Projective Space; 1.6 Group Schemes; 1.6.1 Group Schemes as Functors; 1.6.2 Kernel and Cokernel; 1.6.3 Bialgebras; 1.6.4 Locally Free Groups; 1.6.5 Schematic Representations; 1.7 Cartier Duality; 1.7.1 Duality of Bialgebras; 1.7.2 Duality of Locally Free Groups; 1.8 Quotients by a Group Scheme; 1.8.1 Naive Quotients; 1.8.2 Categorical Quotients; 1.8.3 Geometric Quotients; 1.9 Morphisms; 1.9.1 Topological Definitions; 1.9.2 Diffeo-Geometric Definitions | ||
| 500 | |a 1.9.3 Applications1.10 Cohomology of Coherent Sheaves; 1.10.1 Coherent Cohomology; 1.10.2 Summary of Known Facts; 1.10.3 Cohomological Dimension; 1.11 Descent; 1.11.1 Covering Data; 1.11.2 Descent Data; 1.11.3 Descent of Schemes; 1.12 Barsotti-Tate Groups; 1.12.1 p-Divisible Abelian Sheaf; Exercise; 1.12.2 Connected- Etale Exact Sequence; 1.12.3 Ordinary Barsotti-Tate Group; 1.13 Formal Scheme; 1.13.1 Open Subschemes as Functors; Exercises; 1.13.2 Examples of Formal Schemes; 1.13.3 Deformation Functors; 1.13.4 Connected Formal Groups; 2. Elliptic Curves; 2.1 Curves and Divisors | ||
| 500 | |a 2.1.1 Cartier Divisors2.1.2 Serre-Grothendieck Duality; 2.1.3 Riemann-Roch Theorem; 2.1.4 Relative Riemann-Roch Theorem; 2.2 Elliptic Curves; 2.2.1 Definition; 2.2.2 Abel's Theorem; 2.2.3 Holomorphic Differentials; 2.2.4 Taylor Expansion of Differentials; 2.2.5 Weierstrass Equations of Elliptic Curves; 2.2.6 Moduli of Weierstrass Type; 2.3 Geometric Modular Forms of Level 1; 2.3.1 Functorial Definition; 2.3.2 Coarse Moduli Scheme; 2.3.3 Fields of Moduli; 2.4 Elliptic Curves over C; 2.4.1 Topological Fundamental Groups; 2.4.2 Classical Weierstrass Theory; 2.4.3 Complex Modular Forms | ||
| 500 | |a 2.5 Elliptic Curves over p-Adic Fields2.5.1 Power Series Identities; 2.5.2 Universal Tate Curves; 2.5.3 Etale Covering of Tate Curves; 2.6 Level Structures; 2.6.1 Isogenies; 2.6.2 Level N Moduli Problems; 2.6.3 Generality of Elliptic Curves; 2.6.4 Proof of Theorem 2.6.8; Exercise; 2.6.5 Geometric Modular Forms of Level N; 2.7 L-Functions of Elliptic Curves; 2.7.1 L-Functions over Finite Fields; 2.7.2 Hasse-Weil L-Function; 2.8 Regularity; 2.8.1 Regular Rings; 2.8.2 Regular Moduli Varieties; 2.9 p-Ordinary Moduli Problems; 2.9.1 The Hasse Invariant; 2.9.2 Ordinary Moduli of p-Power Level | ||
| 500 | |a 2.9.3 Irreducibility of p-Ordinary Moduli | ||
| 500 | |a This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti-Tate groups (including formal Li | ||
| 650 | 4 | |a Mathematics | |
| 650 | 7 | |a MATHEMATICS / Geometry / Algebraic |2 bisacsh | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Curves, Elliptic | |
| 650 | 4 | |a Forms, Modular | |
| 650 | 0 | 7 | |a Modulraum |0 (DE-588)4183462-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Elliptische Kurve |0 (DE-588)4014487-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Elliptische Kurve |0 (DE-588)4014487-2 |D s |
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Datensatz im Suchindex
| _version_ | 1804175473991745536 |
|---|---|
| any_adam_object | |
| author | Hida, Haruzo |
| author_facet | Hida, Haruzo |
| author_role | aut |
| author_sort | Hida, Haruzo |
| author_variant | h h hh |
| building | Verbundindex |
| bvnumber | BV043081487 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)794328360 (DE-599)BVBBV043081487 |
| dewey-full | 516.352 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.352 516.3/52 |
| dewey-search | 516.352 516.3/52 |
| dewey-sort | 3516.352 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 2nd ed |
| format | Electronic eBook |
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| id | DE-604.BV043081487 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:51Z |
| institution | BVB |
| isbn | 9789814368650 9814368652 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028505679 |
| oclc_num | 794328360 |
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| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (468 pages) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Hida, Haruzo Verfasser aut Geometric Modular Forms and Elliptic Curves 2nd ed Singapore World Scientific 2011 1 Online-Ressource (468 pages) txt rdacontent c rdamedia cr rdacarrier Preface to the second edition; Preface; Contents; 1. An Algebro-Geometric Tool Box; 1.1 Sheaves; 1.1.1 Sheaves and Presheaves; 1.1.2 Sheafication; 1.1.3 Sheaf Kernel and Cokernel; 1.2 Schemes; 1.2.1 Local Ringed Spaces; 1.2.2 Schemes as Local Ringed Spaces; 1.2.3 Sheaves over Schemes; 1.2.4 Topological Properties of Schemes; 1.3 Projective Schemes; 1.3.1 Graded Rings; 1.3.2 Functor Proj; 1.3.3 Sheaves on Projective Schemes; 1.4 Categories and Functors; 1.4.1 Categories; 1.4.2 Functors; 1.4.3 Schemes as Functors; 1.4.4 Abelian Categories; 1.5 Applications of the Key-Lemma 1.5.1 Sheaf of Differential Forms on Schemes1.5.2 Fiber Products; 1.5.3 Inverse Image of Sheaves; 1.5.4 Affine Schemes; 1.5.5 Morphisms into a Projective Space; 1.6 Group Schemes; 1.6.1 Group Schemes as Functors; 1.6.2 Kernel and Cokernel; 1.6.3 Bialgebras; 1.6.4 Locally Free Groups; 1.6.5 Schematic Representations; 1.7 Cartier Duality; 1.7.1 Duality of Bialgebras; 1.7.2 Duality of Locally Free Groups; 1.8 Quotients by a Group Scheme; 1.8.1 Naive Quotients; 1.8.2 Categorical Quotients; 1.8.3 Geometric Quotients; 1.9 Morphisms; 1.9.1 Topological Definitions; 1.9.2 Diffeo-Geometric Definitions 1.9.3 Applications1.10 Cohomology of Coherent Sheaves; 1.10.1 Coherent Cohomology; 1.10.2 Summary of Known Facts; 1.10.3 Cohomological Dimension; 1.11 Descent; 1.11.1 Covering Data; 1.11.2 Descent Data; 1.11.3 Descent of Schemes; 1.12 Barsotti-Tate Groups; 1.12.1 p-Divisible Abelian Sheaf; Exercise; 1.12.2 Connected- Etale Exact Sequence; 1.12.3 Ordinary Barsotti-Tate Group; 1.13 Formal Scheme; 1.13.1 Open Subschemes as Functors; Exercises; 1.13.2 Examples of Formal Schemes; 1.13.3 Deformation Functors; 1.13.4 Connected Formal Groups; 2. Elliptic Curves; 2.1 Curves and Divisors 2.1.1 Cartier Divisors2.1.2 Serre-Grothendieck Duality; 2.1.3 Riemann-Roch Theorem; 2.1.4 Relative Riemann-Roch Theorem; 2.2 Elliptic Curves; 2.2.1 Definition; 2.2.2 Abel's Theorem; 2.2.3 Holomorphic Differentials; 2.2.4 Taylor Expansion of Differentials; 2.2.5 Weierstrass Equations of Elliptic Curves; 2.2.6 Moduli of Weierstrass Type; 2.3 Geometric Modular Forms of Level 1; 2.3.1 Functorial Definition; 2.3.2 Coarse Moduli Scheme; 2.3.3 Fields of Moduli; 2.4 Elliptic Curves over C; 2.4.1 Topological Fundamental Groups; 2.4.2 Classical Weierstrass Theory; 2.4.3 Complex Modular Forms 2.5 Elliptic Curves over p-Adic Fields2.5.1 Power Series Identities; 2.5.2 Universal Tate Curves; 2.5.3 Etale Covering of Tate Curves; 2.6 Level Structures; 2.6.1 Isogenies; 2.6.2 Level N Moduli Problems; 2.6.3 Generality of Elliptic Curves; 2.6.4 Proof of Theorem 2.6.8; Exercise; 2.6.5 Geometric Modular Forms of Level N; 2.7 L-Functions of Elliptic Curves; 2.7.1 L-Functions over Finite Fields; 2.7.2 Hasse-Weil L-Function; 2.8 Regularity; 2.8.1 Regular Rings; 2.8.2 Regular Moduli Varieties; 2.9 p-Ordinary Moduli Problems; 2.9.1 The Hasse Invariant; 2.9.2 Ordinary Moduli of p-Power Level 2.9.3 Irreducibility of p-Ordinary Moduli This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms. The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given. In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction. In this new second edition, a detailed description of Barsotti-Tate groups (including formal Li Mathematics MATHEMATICS / Geometry / Algebraic bisacsh Mathematik Curves, Elliptic Forms, Modular Modulraum (DE-588)4183462-8 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Modulraum (DE-588)4183462-8 s 1\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457157 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Hida, Haruzo Geometric Modular Forms and Elliptic Curves Mathematics MATHEMATICS / Geometry / Algebraic bisacsh Mathematik Curves, Elliptic Forms, Modular Modulraum (DE-588)4183462-8 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| subject_GND | (DE-588)4183462-8 (DE-588)4014487-2 |
| title | Geometric Modular Forms and Elliptic Curves |
| title_auth | Geometric Modular Forms and Elliptic Curves |
| title_exact_search | Geometric Modular Forms and Elliptic Curves |
| title_full | Geometric Modular Forms and Elliptic Curves |
| title_fullStr | Geometric Modular Forms and Elliptic Curves |
| title_full_unstemmed | Geometric Modular Forms and Elliptic Curves |
| title_short | Geometric Modular Forms and Elliptic Curves |
| title_sort | geometric modular forms and elliptic curves |
| topic | Mathematics MATHEMATICS / Geometry / Algebraic bisacsh Mathematik Curves, Elliptic Forms, Modular Modulraum (DE-588)4183462-8 gnd Elliptische Kurve (DE-588)4014487-2 gnd |
| topic_facet | Mathematics MATHEMATICS / Geometry / Algebraic Mathematik Curves, Elliptic Forms, Modular Modulraum Elliptische Kurve |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=457157 |
| work_keys_str_mv | AT hidaharuzo geometricmodularformsandellipticcurves |