Rigid analytic geometry and its applications:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | German |
| Veröffentlicht: |
Boston
Birkhäuser
2004
|
| Schriftenreihe: | Progress in mathematics
218 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xi, 296 Seiten |
| ISBN: | 9780817642068 0817642064 3764342064 |
Internformat
MARC
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| 001 | BV024618075 | ||
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| 100 | 1 | |a Fresnel, Jean |d 1939- |e Verfasser |0 (DE-588)1077855257 |4 aut | |
| 245 | 1 | 0 | |a Rigid analytic geometry and its applications |c Jean Fresnel ; Marius van der Put |
| 264 | 1 | |a Boston |b Birkhäuser |c 2004 | |
| 264 | 4 | |c © 2004 | |
| 300 | |a xi, 296 Seiten | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Progress in mathematics |v 218 | |
| 650 | 4 | |a Analytischer Raum | |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analytische Stellenalgebra |0 (DE-588)4628801-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Mannigfaltigkeit |0 (DE-588)4128509-8 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Analytische Geometrie |0 (DE-588)4001867-2 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
| 689 | 0 | 1 | |a Algebraische Mannigfaltigkeit |0 (DE-588)4128509-8 |D s |
| 689 | 0 | 2 | |a Analytische Stellenalgebra |0 (DE-588)4628801-6 |D s |
| 689 | 0 | 3 | |a Analytische Geometrie |0 (DE-588)4001867-2 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Put, Marius van der |d 1941- |e Verfasser |0 (DE-588)115533249 |4 aut | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-1-4612-0041-3 |
| 830 | 0 | |a Progress in mathematics |v 218 |w (DE-604)BV000004120 |9 218 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-018590245 | ||
Datensatz im Suchindex
| _version_ | 1804140637411344384 |
|---|---|
| adam_text | Contents
Preface
................................. ix
1
Valued Fields and Normed Spaces
1
1.1
Valued fields
........................... 1
1.2
Banach spaces and Banach algebras
.............. 4
2
The
Projective
Line
13
2.1
Some definitions
......................... 13
2.2
Holomorphic functions on an affinoid subset
......... 15
2.3
The residue theorem
...................... 22
2.4
The Grothendieck topology on
Ρ
............... 25
2.5
Some sheaves on
Ρ
....................... 30
2.6
Analytic subspaces of
Ρ
.................... 33
2.7
Cohomology on an analytic subspace of
Ρ
.......... 37
3
Affinoid Algebras
45
3.1
Definition of an affinoid algebra
................ 46
3.2
Consequences of the
Weierstrass
theorem
........... 48
3.3
Affinoid spaces, Examples
................... 51
3.4
Properties of the spectral (semi-)norm
............ 55
3.5
Integral extensions of affinoid algebras
............ 59
3.6
The differential module
fž^
,k
................. 63
3.7
Products of affinoid spaces,
Picard
groups
.......... 66
vi
Contents
4
Rigid Spaces
71
4.1
Rational subsets
......................... 71
4.2
The weak G-topology and Tate s theorem
.......... 77
4.3
General rigid spaces
....................... 81
4.4
Sheaves on a rigid space
.................... 86
4.5
Coherent analytic sheaves
................... 87
4.6
The sheaf of meromorphic functions
.............. 91
4.7
Rigid vector bundles
...................... 97
4.8
Analytic reductions and formal schemes
............ 99
4.9
Analytic reductions of a subspace of Pj.
.......... 107
4.10
Separated and proper rigid spaces
............... 110
5
Curves and Their Reductions
121
5.1
The
Tate
curve
......................... 121
5.2
Néron
models for abelian varieties
............... 133
5.3
The
Néron
model of an elliptic curve
............. 136
5.4
Mumford curves and Schottky groups
............. 140
5.5
Stable reduction of curves
................... 142
5.6
A rigid proof of stable reduction for curves
.......... 147
5.7
The universal analytic covering of a curve
.......... 160
6
Abelian Varieties
165
6.1
The complex case
........................ 165
6.2
The non-archimedean case
................... 167
6.3
The analytification of an algebraic torus
........... 167
6.4
Lattices and analytic tori
.................... 170
6.5
Meromorphic functions on an analytic torus
......... 172
6.6
Analytic tori and abelian varieties
............... 174
6.7
Néron
models and uniformization
............... 177
6.7.1
Néron
model for an abelian variety of the form
Τ
. . 177
6.7.2
Rigid construction of more general abelian varieties
. 180
6.7.3
Stable reduction for abelian varieties
......... 184
6.7.4
Uniformization of a Jacobian variety
......... 185
7
Points of Rigid Spaces,
Rigid Cohomology
191
7.1
Points and sheaves on an affinoid space
............ 192
7.2
Explicit examples in dimension
1 ............... 203
7.3
V(X) and the reductions of X
................. 206
7.4
Base change for overconvergent sheaves
............ 208
7.5
Overconvergent affinoid spaces
................. 214
7.6
Monsky-Washnitzer cohomology
................ 224
7.7
Rigid cohomology
........................ 236
Contents
vii
8
Etale Cohomology
of Rigid Spaces
239
8.1
Etale morphisms
......................... 240
8.2
The
étale
site
.......................... 244
8.3
Etale
points, overconvergent
étale
sheaves
.......... 248
8.4
Etale
cohomology in dimension
1 ............... 252
8.5
Higher dimensional rigid spaces
................ 255
9
Covers of Algebraic Curves
259
9.1
Introducing the problem
.................... 259
9.2
I. Serre s result
......................... 263
9.3
II. Rigid construction of coverings
............... 264
9.3.1
GAGA for coherent sheaves on
Ρ
........... 265
9.3.2
Covers
.......................... 267
9.3.3
Ramified coverings of P^
............... 269
9.4
III. Reductions of curves modulo
ρ
.............. 272
References
............................... 275
List of Notation
........................... 289
Index
.................................. 293
|
| any_adam_object | 1 |
| author | Fresnel, Jean 1939- Put, Marius van der 1941- |
| author_GND | (DE-588)1077855257 (DE-588)115533249 |
| author_facet | Fresnel, Jean 1939- Put, Marius van der 1941- |
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| classification_tum | MAT 144f |
| ctrlnum | (OCoLC)248855183 (DE-599)BVBBV024618075 |
| dewey-full | 516.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.3 |
| dewey-search | 516.3 |
| dewey-sort | 3516.3 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
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| id | DE-604.BV024618075 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:03:09Z |
| institution | BVB |
| isbn | 9780817642068 0817642064 3764342064 |
| language | German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018590245 |
| oclc_num | 248855183 |
| open_access_boolean | |
| owner | DE-83 DE-739 DE-384 DE-11 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-188 |
| owner_facet | DE-83 DE-739 DE-384 DE-11 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-188 |
| physical | xi, 296 Seiten |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Birkhäuser |
| record_format | marc |
| series | Progress in mathematics |
| series2 | Progress in mathematics |
| spelling | Fresnel, Jean 1939- Verfasser (DE-588)1077855257 aut Rigid analytic geometry and its applications Jean Fresnel ; Marius van der Put Boston Birkhäuser 2004 © 2004 xi, 296 Seiten txt rdacontent n rdamedia nc rdacarrier Progress in mathematics 218 Analytischer Raum Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Analytische Stellenalgebra (DE-588)4628801-6 gnd rswk-swf Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd rswk-swf Analytische Geometrie (DE-588)4001867-2 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Algebraische Mannigfaltigkeit (DE-588)4128509-8 s Analytische Stellenalgebra (DE-588)4628801-6 s Analytische Geometrie (DE-588)4001867-2 s DE-604 Put, Marius van der 1941- Verfasser (DE-588)115533249 aut Erscheint auch als Online-Ausgabe 978-1-4612-0041-3 Progress in mathematics 218 (DE-604)BV000004120 218 Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018590245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fresnel, Jean 1939- Put, Marius van der 1941- Rigid analytic geometry and its applications Progress in mathematics Analytischer Raum Algebraische Geometrie (DE-588)4001161-6 gnd Analytische Stellenalgebra (DE-588)4628801-6 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4628801-6 (DE-588)4128509-8 (DE-588)4001867-2 |
| title | Rigid analytic geometry and its applications |
| title_auth | Rigid analytic geometry and its applications |
| title_exact_search | Rigid analytic geometry and its applications |
| title_full | Rigid analytic geometry and its applications Jean Fresnel ; Marius van der Put |
| title_fullStr | Rigid analytic geometry and its applications Jean Fresnel ; Marius van der Put |
| title_full_unstemmed | Rigid analytic geometry and its applications Jean Fresnel ; Marius van der Put |
| title_short | Rigid analytic geometry and its applications |
| title_sort | rigid analytic geometry and its applications |
| topic | Analytischer Raum Algebraische Geometrie (DE-588)4001161-6 gnd Analytische Stellenalgebra (DE-588)4628801-6 gnd Algebraische Mannigfaltigkeit (DE-588)4128509-8 gnd Analytische Geometrie (DE-588)4001867-2 gnd |
| topic_facet | Analytischer Raum Algebraische Geometrie Analytische Stellenalgebra Algebraische Mannigfaltigkeit Analytische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018590245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000004120 |
| work_keys_str_mv | AT fresneljean rigidanalyticgeometryanditsapplications AT putmariusvander rigidanalyticgeometryanditsapplications |