Algebraic and analytic geometry:
Gespeichert in:
1. Verfasser: | |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Cambridge [u.a.]
Cambridge Univ. Press
2007
|
Ausgabe: | 1. publ. |
Schriftenreihe: | London Mathematical Society lecture notes series
345 |
Schlagworte: | |
Online-Zugang: | Inhaltsverzeichnis |
Beschreibung: | XII, 420 S. graph. Darst. |
ISBN: | 9780521709835 |
Internformat
MARC
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100 | 1 | |a Neeman, Amnon |d 1957- |e Verfasser |0 (DE-588)112427227 |4 aut | |
245 | 1 | 0 | |a Algebraic and analytic geometry |c Amnon Neeman |
250 | |a 1. publ. | ||
264 | 1 | |a Cambridge [u.a.] |b Cambridge Univ. Press |c 2007 | |
300 | |a XII, 420 S. |b graph. Darst. | ||
336 | |b txt |2 rdacontent | ||
337 | |b n |2 rdamedia | ||
338 | |b nc |2 rdacarrier | ||
490 | 1 | |a London Mathematical Society lecture notes series |v 345 | |
650 | 4 | |a Geometry, Algebraic | |
650 | 4 | |a Geometry, Analytic | |
650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
655 | 7 | |0 (DE-588)4151278-9 |a Einführung |2 gnd-content | |
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Datensatz im Suchindex
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adam_text | Contents
Preface page ix
1 Introduction 1
1.1 Algebraic and analytic subspaces 4
1.2 Elliptic curves 7
1.3 Notation 10
2 Manifolds 11
2.1 Manifolds defined in the traditional way 11
2.2 Sheaves of rings and ringed spaces 14
2.3 There are not many maps of ringed spaces 19
2.4 The sheaf theoretic definition of a manifold 23
3 Schemes 26
3.1 The space Spec(/?) 27
3.2 A basis for the Zariski topology 29
3.3 Localization of rings 31
3.4 The sheaf R on Spec(«) 36
3.5 A return to the world of simple examples 44
3.6 Maps of ringed spaces (Spec(S), S) + (Spec(R), R) 50
3.7 Some immediate consequences 54
3.8 A reminder of Hilbert s Nullstellensatz 59
3.9 Ringed spaces over C 60
3.10 Schemes of finite type over C 64
4 The complex topology 71
4.1 Synopsis of the main results 71
4.2 The subspace Max(X) C X 72
v
vi Contents
4.3 The correspondence between maximal ideals and
p : R + C 77
4.4 The special case of the polynomial ring 79
4.5 The complex topology on MaxSpec(i?) 83
4.6 The complex topology on schemes 91
5 The analytification of a scheme 100
5.1 Synopsis of the main results 100
5.2 The Hilbert Basis Theorem 102
5.3 The sheaf of analytic functions on an affine scheme 104
5.4 A reminder about Frechet spaces 111
5.5 The ring of analytic functions as a completion 116
5.6 Allowing the ring and the generators to vary 120
5.7 Affine schemes, done without coordinates 132
5.8 In the world of elementary examples 142
5.9 Gluing it all 159
6 The high road to analytification 162
6.1 A coordinate free approach to polydiscs 162
6.2 The high road to the complex topology 166
6.3 The high road to the sheaf of analytic functions 167
7 Coherent sheaves 170
7.1 Sheaves of modules on a ringed space 171
7.2 The sheaves M 179
7.3 Localization for modules 181
7.4 The sheaf of modules more explicitly 183
7.5 Morphisms of sheaves 185
7.6 Coherent algebraic sheaves 190
7.7 Coherent analytic sheaves 200
7.8 The analytification of coherent algebraic sheaves 201
7.9 The statement of GAGA 207
8 Projective space the statements 211
8.1 Products of affine schemes 213
8.2 Affine group schemes 216
8.3 Affine group schemes acting on affine schemes 221
8.4 The action of the group of closed points 228
8.5 Back to the world of the concrete 236
8.6 Quotients of affine schemes 239
8.7 Sheaves on the quotient 245
8.8 The main results 248
8.9 What it all means, in a concrete example 253
Contents vii
9 Projective space the proofs 270
9.1 A reminder of symmetric powers 272
9.2 Generators 273
9.3 Finite dimensional representations of C* 282
9.4 The finite generation of the ring of invariants 289
9.5 The topological facts about n : X X/G 292
9.6 The sheaves on X/G 299
9.7 Two technical lemmas 303
9.8 The global statement about coherent sheaves 310
9.9 The case of the trivial group 323
10 The proof of GAGA 325
10.1 The sheaves O(m) 327
10.2 Another visit to the concrete world 329
10.3 Maps between the sheaves O(m) 337
10.4 The coherent analytic version 342
10.5 Sheaf cohomology 349
10.6 GAGA in terms of cohomology 355
10.7 The first half of GAGA 369
10.8 Skyscraper sheaves 372
10.9 Skyscraper sheaves on P 378
10.10 The second half of GAGA 383
Appendix 1 The proofs concerning analytification 392
Bibliography 409
Glossary 410
Index 413
|
adam_txt |
Contents
Preface page ix
1 Introduction 1
1.1 Algebraic and analytic subspaces 4
1.2 Elliptic curves 7
1.3 Notation 10
2 Manifolds 11
2.1 Manifolds defined in the traditional way 11
2.2 Sheaves of rings and ringed spaces 14
2.3 There are not many maps of ringed spaces 19
2.4 The sheaf theoretic definition of a manifold 23
3 Schemes 26
3.1 The space Spec(/?) 27
3.2 A basis for the Zariski topology 29
3.3 Localization of rings 31
3.4 The sheaf R on Spec(«) 36
3.5 A return to the world of simple examples 44
3.6 Maps of ringed spaces (Spec(S), S) + (Spec(R), R) 50
3.7 Some immediate consequences 54
3.8 A reminder of Hilbert's Nullstellensatz 59
3.9 Ringed spaces over C 60
3.10 Schemes of finite type over C 64
4 The complex topology 71
4.1 Synopsis of the main results 71
4.2 The subspace Max(X) C X 72
v
vi Contents
4.3 The correspondence between maximal ideals and
p : R + C 77
4.4 The special case of the polynomial ring 79
4.5 The complex topology on MaxSpec(i?) 83
4.6 The complex topology on schemes 91
5 The analytification of a scheme 100
5.1 Synopsis of the main results 100
5.2 The Hilbert Basis Theorem 102
5.3 The sheaf of analytic functions on an affine scheme 104
5.4 A reminder about Frechet spaces 111
5.5 The ring of analytic functions as a completion 116
5.6 Allowing the ring and the generators to vary 120
5.7 Affine schemes, done without coordinates 132
5.8 In the world of elementary examples 142
5.9 Gluing it all 159
6 The high road to analytification 162
6.1 A coordinate free approach to polydiscs 162
6.2 The high road to the complex topology 166
6.3 The high road to the sheaf of analytic functions 167
7 Coherent sheaves 170
7.1 Sheaves of modules on a ringed space 171
7.2 The sheaves M 179
7.3 Localization for modules 181
7.4 The sheaf of modules more explicitly 183
7.5 Morphisms of sheaves 185
7.6 Coherent algebraic sheaves 190
7.7 Coherent analytic sheaves 200
7.8 The analytification of coherent algebraic sheaves 201
7.9 The statement of GAGA 207
8 Projective space the statements 211
8.1 Products of affine schemes 213
8.2 Affine group schemes 216
8.3 Affine group schemes acting on affine schemes 221
8.4 The action of the group of closed points 228
8.5 Back to the world of the concrete 236
8.6 Quotients of affine schemes 239
8.7 Sheaves on the quotient 245
8.8 The main results 248
8.9 What it all means, in a concrete example 253
Contents vii
9 Projective space the proofs 270
9.1 A reminder of symmetric powers 272
9.2 Generators 273
9.3 Finite dimensional representations of C* 282
9.4 The finite generation of the ring of invariants 289
9.5 The topological facts about n : X X/G 292
9.6 The sheaves on X/G 299
9.7 Two technical lemmas 303
9.8 The global statement about coherent sheaves 310
9.9 The case of the trivial group 323
10 The proof of GAGA 325
10.1 The sheaves O(m) 327
10.2 Another visit to the concrete world 329
10.3 Maps between the sheaves O(m) 337
10.4 The coherent analytic version 342
10.5 Sheaf cohomology 349
10.6 GAGA in terms of cohomology 355
10.7 The first half of GAGA 369
10.8 Skyscraper sheaves 372
10.9 Skyscraper sheaves on P" 378
10.10 The second half of GAGA 383
Appendix 1 The proofs concerning analytification 392
Bibliography 409
Glossary 410
Index 413 |
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institution | BVB |
isbn | 9780521709835 |
language | English |
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physical | XII, 420 S. graph. Darst. |
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spelling | Neeman, Amnon 1957- Verfasser (DE-588)112427227 aut Algebraic and analytic geometry Amnon Neeman 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XII, 420 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier London Mathematical Society lecture notes series 345 Geometry, Algebraic Geometry, Analytic Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Algebraische Geometrie (DE-588)4001161-6 s DE-604 London Mathematical Society lecture notes series 345 (DE-604)BV000000130 345 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015985688&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Neeman, Amnon 1957- Algebraic and analytic geometry London Mathematical Society lecture notes series Geometry, Algebraic Geometry, Analytic Algebraische Geometrie (DE-588)4001161-6 gnd |
subject_GND | (DE-588)4001161-6 (DE-588)4151278-9 |
title | Algebraic and analytic geometry |
title_auth | Algebraic and analytic geometry |
title_exact_search | Algebraic and analytic geometry |
title_exact_search_txtP | Algebraic and analytic geometry |
title_full | Algebraic and analytic geometry Amnon Neeman |
title_fullStr | Algebraic and analytic geometry Amnon Neeman |
title_full_unstemmed | Algebraic and analytic geometry Amnon Neeman |
title_short | Algebraic and analytic geometry |
title_sort | algebraic and analytic geometry |
topic | Geometry, Algebraic Geometry, Analytic Algebraische Geometrie (DE-588)4001161-6 gnd |
topic_facet | Geometry, Algebraic Geometry, Analytic Algebraische Geometrie Einführung |
url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015985688&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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