Etale cohomology theory:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Singapore [u.a.]
World Scientific
2011
|
| Series: | Nankai Tracts in Mathematics
13 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 611 S. |
| ISBN: | 9789814307727 9814307726 |
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MARC
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Record in the Search Index
| _version_ | 1804143840322387968 |
|---|---|
| adam_text | Contents
Preface
v
1.
Descent Theory
1
1.1
Flat Modules
......................... 1
1.2
Faithfully Flat Modules
................... 3
1.3
Local Criteria for Flatness
.................. 10
1.4
Constructible Sets
...................... 15
1.5
Flat Morphisms
........................ 18
1.6
Descent of Quasi-coherent Sheaves
............. 21
1.7
Descent of Properties of Morphisms
............ 28
1.8
Descent of Schemes
...................... 35
1.9
Quasi-finite Morphisms
................... 41
1.10
Passage to Limit
....................... 45
2.
Etale
Morphisms and Smooth Morphisms
59
2.1
The Sheaf of Relative Differentials
............. 59
2.2
Unramified Morphisms
.................... 64
2.3
Etale
Morphisms
....................... 66
2.4
Smooth Morphisms
...................... 73
2.5
Jacobian Criterion
...................... 75
2.6
Infinitesimal Liftings of Morphisms
............. 83
2.7
Direct Limits and Inverse Limits
.............. 87
2.8
Henselization
......................... 90
2.9
Etale
Morphisms between Normal Schemes
........ 113
3.
Etale
Fundamental Groups
117
viii
Etale Cohomology
Theory
3.1
Finite Group
Actions on Schemes
.............. 117
3.2
Etale
Covering Spaces and Fundamental Groups
..... 121
3.3
Functorial Properties of Fundamental Groups
....... 131
4.
Group Cohomology and Galois Cohomology
139
4.1
Group Cohomology
...................... 139
4.2
Profinite
Groups
....................... 146
4.3
Cohomology of
Profinite
Groups
.............. 152
4.4
Cohomological Dimensions
.................. 161
4.5
Galois Cohomology
...................... 164
5.
Etale
Cohomology
171
5.1
Presheaves and
Cech
Cohomology
............. 171
5.2
Etale
Sheaves
......................... 176
5.3
Stalks of Sheaves
....................... 193
5.4
Recollement
of Sheaves
.................... 201
5.5
The Functor
ƒ......................... 205
5.6
Etale
Cohomology
...................... 210
5.7
Calculation of
Etale
Cohomology
.............. 222
5.8
Constructible
Sheaves
.................... 245
5.9
Passage to Limit
....................... 257
6.
Derived Categories and Derived Functors
267
6.1
Triangulated Categories
................... 267
6.2
Derived Categories
...................... 272
6.3
Derived Functors
....................... 279
6.4
ñHom(-,-)
and
-
®^
-.................. 287
6.5
Way-out Functors
...................... 303
7.
Base Change Theorems
311
7.1
Divisors
............................ 311
7.2
Cohomology of Curves
.................... 317
7.3
Proper Base Change Theorem
................ 331
7.4
Cohomology with Proper Support
............. 350
7.5
Cohomological Dimension of Rf*
.............. 368
7.6
Local Acyclicity
........................ 377
7.7
Smooth Base Change Theorem
............... 391
7.8
Finiteness of
Rf
....................... 406
Contents ix
8.
Duality
411
8.1
Extensions of Henselian Discrete Valuation Rings
..... 411
8.2
Trace Morphisms
....................... 419
8.3
Duality for Curves
...................... 432
8.4
The Functor Rf
....................... 443
8.5
Poincaré
Duality
....................... 462
8.6
Cohomology Classes of Algebraic Cycles
.......... 478
9.
Finiteness Theorems
497
9.1
Sheaves with Group Actions
................. 497
9.2
Nearby Cycle and Vanishing Cycle
............. 502
9.3
Generic Base Change Theorem and
Generic Local Acyclicity
................... 509
9.4
Finiteness of
ДФ,,
...................... 517
9.5
Finiteness Theorems
..................... 521
9.6
Biduality
........................... 526
10.
¿-adic
Cohomology
531
10.1
Adic
Formalism
........................ 531
10.2
Grothendieck-Ogg-Shafarevich Formula
.......... 566
10.3
Frobenius Correspondences
................. 585
10.4
Lefschetz Trace Formula
................... 592
10.5
Grothendieck s Formula of ¿-functions
........... 603
Bibliography
607
Index
609
|
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| building | Verbundindex |
| bvnumber | BV037233266 |
| classification_rvk | SK 320 |
| classification_tum | MAT 552f |
| ctrlnum | (OCoLC)729935344 (DE-599)BVBBV037233266 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV037233266 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T22:54:03Z |
| institution | BVB |
| isbn | 9789814307727 9814307726 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-021146889 |
| oclc_num | 729935344 |
| open_access_boolean | |
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| owner_facet | DE-11 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-703 DE-91G DE-BY-TUM |
| physical | IX, 611 S. |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| series | Nankai Tracts in Mathematics |
| series2 | Nankai tracts in mathematics |
| spelling | Fu, Lei Verfasser aut Etale cohomology theory Lei Fu Singapore [u.a.] World Scientific 2011 IX, 611 S. txt rdacontent n rdamedia nc rdacarrier Nankai tracts in mathematics 13 Etalkohomologie (DE-588)4153071-8 gnd rswk-swf Etalkohomologie (DE-588)4153071-8 s DE-604 Nankai Tracts in Mathematics 13 (DE-604)BV014017593 13 Digitalisierung UB Bayreuth application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021146889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Fu, Lei Etale cohomology theory Nankai Tracts in Mathematics Etalkohomologie (DE-588)4153071-8 gnd |
| subject_GND | (DE-588)4153071-8 |
| title | Etale cohomology theory |
| title_auth | Etale cohomology theory |
| title_exact_search | Etale cohomology theory |
| title_full | Etale cohomology theory Lei Fu |
| title_fullStr | Etale cohomology theory Lei Fu |
| title_full_unstemmed | Etale cohomology theory Lei Fu |
| title_short | Etale cohomology theory |
| title_sort | etale cohomology theory |
| topic | Etalkohomologie (DE-588)4153071-8 gnd |
| topic_facet | Etalkohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=021146889&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV014017593 |
| work_keys_str_mv | AT fulei etalecohomologytheory |