Algebraic curves and one-dimensional fields:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Courant Inst. of Math. Sciences [u.a.]
2002
|
| Schriftenreihe: | Courant lecture notes in mathematics
8 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XI, 214 S. graph. Darst. |
| ISBN: | 0821828622 |
Internformat
MARC
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| 100 | 1 | |a Bogomolov, Fedor A. |d 1946- |e Verfasser |0 (DE-588)129921637 |4 aut | |
| 245 | 1 | 0 | |a Algebraic curves and one-dimensional fields |c Fedor Bogomolov ; Tihomir Petrov |
| 264 | 1 | |a New York, NY |b Courant Inst. of Math. Sciences [u.a.] |c 2002 | |
| 300 | |a XI, 214 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Courant lecture notes in mathematics |v 8 | |
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| 830 | 0 | |a Courant lecture notes in mathematics |v 8 |w (DE-604)BV012714106 |9 8 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-009952675 | ||
Datensatz im Suchindex
| _version_ | 1804129420776046592 |
|---|---|
| adam_text | Contents
Preface ix
Chapter 1. Algebraic Preliminaries 1
1.1. Rings 1
1.2. Fields and Field Extensions 8
1.3. Modules 29
1.4. Noetherian Rings 34
1.5. Artinian Rings 36
1.6. Integral Extensions of Rings 37
1.7. One Dimensional Rings and Fields 40
Chapter 2. From Algebra to Geometry 43
2.1. Affine Algebraic Varieties 43
2.2. Projective Varieties 49
2.3. Rational Functions and Rational Maps 50
2.4. Abstract Algebraic Varieties 52
2.5. Dimension of Varieties 54
2.6. Local Rings 55
Chapter 3. Geometry of Dimension One 61
3.1. Valuations 61
3.2. Completions 65
3.3. Extensions of Complete Fields and Valuations 73
3.4. Normalization 82
3.5. Construction of the Curve CK 83
3.6. Properties of the Curve CK 85
3.7. Nonrational Fields of Dimension One 87
3.8. Description of the Normal Subrings 88
3.9. All Subrings in Dimension One 91
Chapter 4. Divisors and Line Bundles 95
4.1. Divisors and Picard Group 95
4.2. Effective Divisors 99
4.3. Divisors and Modules on Affine Curves 100
4.4. Maps Between Groups of Divisors and Luroth s Theorem 106
4.5. Line Bundles on Curves 108
4.6. Sections of a Line Bundle 113
viii CONTENTS
4.7. Line Bundles on P 117
Chapter 5. Vector Bundles, Coherent Sheaves, and Cohomology 119
5.1. Vector Bundles U9
5.2. Vector Bundles on Smooth Affine Curves 123
5.3. Coherent Sheaves I26
5.4. Torsion Sheaves 129
5.5. Extensions of Vector Bundles 132
5.6. Zero Cohomology 136
5.7. First Cohomology 141
Chapter 6. Vector Bundles on P1 I49
6.1. Line Bundles on P1 149
6.2. Vector Bundles on P1 152
6.3. The Riemann Roch Theorem for P1 155
6.4. Exact Cohomology Sequence on P1 157
Chapter 7. General Theory of Curves 163
7.1. Direct Image 163
7.2. The Riemann Roch Formula 167
7.3. Cohomology Computations 171
Chapter 8. Elliptic Curves I73
8.1. Line Bundles on Elliptic Curves 173
8.2. Elliptic Curves as Plane Cubic Curves 174
8.3. Hyperellipticity and the Weierstrass Form 176
8.4. The Riemann Roch Theorem for Elliptic Curves 181
Chapter 9. The Riemann Roch Theorem 183
9.1. Construction of the Map h * 183
9.2. Algebraicity of the Map hK 189
9.3. The Riemann Roch Theorem l91
9.4. Geometrical Implications of the Riemann Roch Theorem I92
Chapter 10. Curves over Arithmetic Fields 197
10.1. The Construction of Belyi over Q 198
10.2. The Construction of Belyi for Field Extensions 200
10.3. Field of Definition of Ramified Coverings 202
10.4. Another Proof of Belyi s Theorem 203
10.5. Triangulations Coming from Ramified Coverings 205
Bibliography 209
Index 211
|
| any_adam_object | 1 |
| author | Bogomolov, Fedor A. 1946- Petrov, Tihomir |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 |
| ctrlnum | (OCoLC)300765458 (DE-599)BVBBV014668903 |
| dewey-full | 516.3/52 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3/52 |
| dewey-search | 516.3/52 |
| dewey-sort | 3516.3 252 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T19:04:52Z |
| institution | BVB |
| isbn | 0821828622 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009952675 |
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| physical | XI, 214 S. graph. Darst. |
| publishDate | 2002 |
| publishDateSearch | 2002 |
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| publisher | Courant Inst. of Math. Sciences [u.a.] |
| record_format | marc |
| series | Courant lecture notes in mathematics |
| series2 | Courant lecture notes in mathematics |
| spelling | Bogomolov, Fedor A. 1946- Verfasser (DE-588)129921637 aut Algebraic curves and one-dimensional fields Fedor Bogomolov ; Tihomir Petrov New York, NY Courant Inst. of Math. Sciences [u.a.] 2002 XI, 214 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Courant lecture notes in mathematics 8 Courbes algébriques Courbes algébriques ram Courbes projectives Projektive Kurve (DE-588)4175887-0 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 gnd rswk-swf Algebraische Kurve (DE-588)4001165-3 s DE-604 Projektive Kurve (DE-588)4175887-0 s Petrov, Tihomir Verfasser (DE-588)1308350546 aut Erscheint auch als Online-Ausgabe 978-1-4704-3109-9 Courant lecture notes in mathematics 8 (DE-604)BV012714106 8 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009952675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bogomolov, Fedor A. 1946- Petrov, Tihomir Algebraic curves and one-dimensional fields Courant lecture notes in mathematics Courbes algébriques Courbes algébriques ram Courbes projectives Projektive Kurve (DE-588)4175887-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| subject_GND | (DE-588)4175887-0 (DE-588)4001165-3 |
| title | Algebraic curves and one-dimensional fields |
| title_auth | Algebraic curves and one-dimensional fields |
| title_exact_search | Algebraic curves and one-dimensional fields |
| title_full | Algebraic curves and one-dimensional fields Fedor Bogomolov ; Tihomir Petrov |
| title_fullStr | Algebraic curves and one-dimensional fields Fedor Bogomolov ; Tihomir Petrov |
| title_full_unstemmed | Algebraic curves and one-dimensional fields Fedor Bogomolov ; Tihomir Petrov |
| title_short | Algebraic curves and one-dimensional fields |
| title_sort | algebraic curves and one dimensional fields |
| topic | Courbes algébriques Courbes algébriques ram Courbes projectives Projektive Kurve (DE-588)4175887-0 gnd Algebraische Kurve (DE-588)4001165-3 gnd |
| topic_facet | Courbes algébriques Courbes projectives Projektive Kurve Algebraische Kurve |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009952675&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV012714106 |
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