An invitation to arithmetic geometry:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, R.I.
American Mathematical Society
1996
|
| Schriftenreihe: | Graduate studies in mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XV, 397 S. graph. Darst. |
| ISBN: | 0821802674 |
Internformat
MARC
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| 100 | 1 | |a Lorenzini, Dino |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a An invitation to arithmetic geometry |c Dino Lorenzini |
| 264 | 1 | |a Providence, R.I. |b American Mathematical Society |c 1996 | |
| 300 | |a XV, 397 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Graduate studies in mathematics |v 9 | |
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| 650 | 7 | |a Géométrie algébrique arithmétique |2 ram | |
| 650 | 4 | |a Arithmetical algebraic geometry | |
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Datensatz im Suchindex
| _version_ | 1804125394328092672 |
|---|---|
| adam_text | Contents
Preface xiii
Description of the chapters 1
Chapter I. Integral closure 5
1. Introduction 5
2. Integral elements 9
3. Products of ideals 16
4. Noetherian rings 20
5. Rings of dimension 1 28
6. Dedekind domains 31
Chapter II. Plane curves 35
1. Introduction 35
2. Rings of functions 38
3. Points and maximal ideals 45
4. Morphisms of curves 47
5. Singular points 51
6. Localization 57
7. More on dimension 63
8. Local principal ideal domains 67
9. Localization of modules 71
10. Hilbert s Basis Theorem 76
11. More rings of functions 77
Chapter III. Factorization of ideals 85
1. Introduction 85
2. Unique factorization of ideals 88
3. Ramification index and residual degree 93
4. Explicit factorizations 98
5. Ramified and unramified primes 101
ix
x CONTENTS
6. Simple extensions 105
7. Examples 108
8. Galois extensions 116
9. Galois covers 120
Chapter IV. The discriminants 131
1. Introduction 131
2. The discriminant as a norm 133
3. The discriminant of a basis 138
4. Examples of non simple extensions 141
5. The discriminant ideal 143
6. Norm map on ideals 149
Chapter V. The ideal class group 157
1. Introduction 157
2. Definition of the ideal class group 158
3. Rings with finite quotients 160
4. The case of number fields 163
5. The case of function fields (I) 167
6. Absolute values and valuations 168
7. Archimedian absolute values and the product formula 172
8. The case of function fields (II) 176
9. Valuations and local principal ideal domains 181
10. Nonsingular complete curves 183
Chapter VI. Projective curves 193
1. Introduction 193
2. Projective spaces 194
3. Plane projective curves 199
4. Projective transformations 203
5. Conies 205
6. Projections 206
7. The tangent line at a point of a projective curve 209
8. Functions on a projective curve 213
9. Projective curves and valuations 217
10. The intersection of two projective curves 221
Chapter VII. Nonsingular complete curves 225
1. Introduction 225
2. Nonsingular curves and Dedekind domains, revisited 227
3. Fields of definition and Galois actions on curves 230
4. Function fields 236
5. Morphisms of nonsingular complete curves 244
6. Fields of definition, revisited 252
CONTENTS xi
7. The divisor class group 259
Chapter VIII. Zeta functions 269
1. Introduction 269
2. The Riemann ( function 274
3. ( functions and Euler products 276
4. Power series 277
5. The zeta function of a nonsingular curve 279
6. The rationality of the zeta function 284
7. The functional equation 288
8. Jacobi sums 292
9. Relations between class numbers 296
Chapter IX. The Riemann Roch Theorem 305
1. Introduction 305
2. Laurent expansions 308
3. Riemann s Theorem 310
4. Duality 316
5. Changing the ground field 323
6. The genus of a nonsingular plane curve 327
7. The arithmetical genus 329
8. The Riemann Hurwitz formula 331
9. Maps to projective spaces 333
Chapter X. Frobenius morphisms and the Riemann hypothesis 339
1. Inseparable extensions 339
2. The Frobenius morphisms 344
3. The Frobenius endomorphism 348
4. The Frobenius element at a point of a Galois cover 351
5. The Riemann hypothesis 354
6. End of the proof 358
Chapter XI. Further topics 361
1. Diophantine problems 361
2. Surfaces 362
3. The jacobian variety 363
4. Galois representations 365
5. The characteristic polynomial of Frobenius 366
6. From Gal(Q/Q) to Gal(Fp/Fp) 368
7. ( functions 371
8. Extensions with given Galois groups 373
Chapter XII. Appendix 375
1. Gauss Lemma 375
|
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| illustrated | Illustrated |
| indexdate | 2024-07-09T18:00:52Z |
| institution | BVB |
| isbn | 0821802674 |
| language | English |
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| physical | XV, 397 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Lorenzini, Dino Verfasser aut An invitation to arithmetic geometry Dino Lorenzini Providence, R.I. American Mathematical Society 1996 XV, 397 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 9 Algebraïsche meetkunde gtt Getaltheorie gtt Géométrie algébrique arithmétique ram Arithmetical algebraic geometry Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 gnd rswk-swf Arithmetische Geometrie (DE-588)4131383-5 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Graduate studies in mathematics 9 (DE-604)BV009739289 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007292412&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lorenzini, Dino An invitation to arithmetic geometry Graduate studies in mathematics Algebraïsche meetkunde gtt Getaltheorie gtt Géométrie algébrique arithmétique ram Arithmetical algebraic geometry Algebraische Geometrie (DE-588)4001161-6 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4131383-5 |
| title | An invitation to arithmetic geometry |
| title_auth | An invitation to arithmetic geometry |
| title_exact_search | An invitation to arithmetic geometry |
| title_full | An invitation to arithmetic geometry Dino Lorenzini |
| title_fullStr | An invitation to arithmetic geometry Dino Lorenzini |
| title_full_unstemmed | An invitation to arithmetic geometry Dino Lorenzini |
| title_short | An invitation to arithmetic geometry |
| title_sort | an invitation to arithmetic geometry |
| topic | Algebraïsche meetkunde gtt Getaltheorie gtt Géométrie algébrique arithmétique ram Arithmetical algebraic geometry Algebraische Geometrie (DE-588)4001161-6 gnd Arithmetische Geometrie (DE-588)4131383-5 gnd |
| topic_facet | Algebraïsche meetkunde Getaltheorie Géométrie algébrique arithmétique Arithmetical algebraic geometry Algebraische Geometrie Arithmetische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007292412&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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