Introduction to étale cohomology:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin u.a.
Springer
1994
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | IX, 186 S. grap. Darst. |
| ISBN: | 0387571167 3540571167 9783540571162 |
Staff View
MARC
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| 100 | 1 | |a Tamme, Günter |d 1937-2022 |e Verfasser |0 (DE-588)117726052 |4 aut | |
| 240 | 1 | 0 | |a Einführung in die étale Kohomologie |
| 245 | 1 | 0 | |a Introduction to étale cohomology |c Günter Tamme |
| 264 | 1 | |a Berlin u.a. |b Springer |c 1994 | |
| 300 | |a IX, 186 S. |b grap. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Universitext | |
| 650 | 7 | |a Cohomologie |2 gtt | |
| 650 | 7 | |a Faisceaux, théorie des |2 ram | |
| 650 | 7 | |a Géométrie algébrique |2 ram | |
| 650 | 7 | |a Homologie |2 gtt | |
| 650 | 7 | |a Homologie |2 ram | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Sheaf theory | |
| 650 | 0 | 7 | |a Kohomologietheorie |0 (DE-588)4164610-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Etalkohomologie |0 (DE-588)4153071-8 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1807506024030011392 |
|---|---|
| adam_text |
CONTENTS
CHAPTER
0.
PRELIMINARIES
.
1
§1.
ABELIAN
CATEGORIES
.
1
(1.1)
CATEGORIES
AND
FUNCTORS
.
1
(1.2)
ADDITIVE
CATEGORIES
.
3
(1.3)
ABELIAN
CATEGORIES
.
4
(1.4)
INJECTIVE
OBJECTS
.
6
§2.
HOMOLOGICAL
ALGEBRA
IN
ABELIAN
CATEGORIES
.
9
(2.1)
5-FUNCTORS
.
9
(2.2)
DERIVED
FUNCTORS
.
11
(2.3)
SPECTRAL
SEQUENCES
.
13
§3.
INDUCTIVE
LIMITS
.
17
(3.1)
LIMIT
FUNCTORS
.
17
(3.2)
EXACTNESS
OF
INDUCTIVE
LIMITS
.
19
(3.3)
FINAL
SUBCATEGORIES
.
20
CHAPTER
I.
TOPOLOGIES
AND
SHEAVES
.
23
§1.
TOPOLOGIES
.
23
(1.1)
PRELIMINARIES
.
23
(1.2)
GROTHENDIECK
'
S
NOTION
OF
TOPOLOGY
.
24
(1.3)
EXAMPLES
.
25
§2.
ABELIAN
PRESHEAVES
ON
TOPOLOGIES
.
31
(2.1)
THE
CATEGORY
OF
ABELIAN
PRESHEAVES
.
31
(2.2)
CECH-COHOMOLOGY
.
32
(2.3)
THE
FUNCTORS
F
P
AND
F
P
.
41
§3.
ABELIAN
SHEAVES
ON
TOPOLOGIES
.
46
(3.1)
THE
ASSOCIATED
SHEAF
OF
A
PRESHEAF
.
46
(3.2)
THE
CATEGORY
OF
ABELIAN
SHEAVES
.
50
(3.3)
COHOMOLOGY
OF
ABELIAN
SHEAVES
.
54
(3.4)
THE
SPECTRAL
SEQUENCES
FOR
CECH
COHOMOLOGY
.
56
(3.5)
FLABBY
SHEAVES
.
61
(3.6)
THE
FUNCTORS
F
A
AND
F
A
.
63
VIII
CONTENTS
(3.7)
THE
LERAY
SPECTRAL
SEQUENCES
.
69
(3.8)
LOCALIZATION
.
73
(3.9)
THE
COMPARISON
LEMMA
.
75
(3.10)
NOETHERIAN
TOPOLOGIES
.
79
(3.11)
COMMUTATION
OF
THE
FUNCTORS
H
Q
(U,
YY
)
WITH
PSEUDOFILTERED
INDUCTIVE
LIMITS
.
81
CHAPTER
II.
ETALE
COHOMOLOGY
.
85
§1.
THE
LILTALE
SITE
OF
A
SCHEME
.
85
(1.1)
ETALE
MORPHISMS
.
85
(1.2)
THE
ETALE
SITE
.
86
(1.3)
THE
RELATION
BETWEEN
ETALE
AND
ZARISKI
COHOMOLOGY
.
86
(1.4)
THE
FUNCTORS
/*
AND
F*
.87
(1.5)
THE
RESTRICTED
ETALE
SITE
.
90
§2.
THE
CASE
X
=
SPEC(K)
.
92
§3.
EXAMPLES
OF
ETALE
SHEAVES
.
95
(3.1)
REPRESENTABLE
SHEAVES
.
95
(3.2)
ETALE
SHEAVES
OF
OX-MODULES
.
100
(3.3)
APPENDIX:
THE
BIG
ETALE
SITE
.
101
§4.
THE
THEORIES
OF
ARTIN-SCHREIER
AND
OF
KUMMER
.
103
(4.1)
THE
GROUPS
H
Q
(X,
(G)X)
.
103
(4.2)
THE
ARTIN-SCHREIER
SEQUENCE
.
105
(4.3)
THE
GROUPS
H
Q
(X,
(G
M
)
X
)
.
106
(4.4)
THE
KUMMER
SEQUENCE
.
109
(4.5)
THE
SHEAF
OF
DIVISORS
ON
X&,
.
ILL
§5.
STALKS
OF
ETALE
SHEAVES
.
114
§6.
STRICT
LOCALIZATIONS
.
120
(6.1)
HENSELIAN
RINGS
AND
STRICTLY
LOCAL
RINGS
.
120
(6.2)
STRICT
LOCALIZATION
OF
A
SCHEME
.
123
(6.3)
ETALE
COHOMOLOGY
ON
PROJECTIVE
LIMITS
OF
SCHEMES
.
125
(6.4)
THE
STALKS
OF
R
Q
F(F)
.
127
§7.
THE
ARTIN
SPECTRAL
SEQUENCE
.
130
§8.
THE
DECOMPOSITION
THEOREM.
RELATIVE
COHOMOLOGY
.
134
(8.1)
THE
DECOMPOSITION
THEOREM
.
134
(8.2)
THE
FUNCTORS
JI
AND
I
!
.
141
(8.3)
RELATIVE
COHOMOLOGY
.
144
CONTENTS
IX
§9.
TORSION
SHEAVES,
LOCALLY
CONSTANT
SHEAVES,
CONSTRUCTIBLE
SHEAVES
.
146
(9.1)
TORSION
SHEAVES
.
146
(9.2)
LOCALLY
CONSTANT
SHEAVES
.
151
(9.3)
CONSTRUCTIBLE
SHEAVES
.
154
§10.
ETALE
COHOMOLOGY
OF
CURVES
.
157
(10.1)
SKYSCRAPER
SHEAVES
.
157
(10.2)
THE
COHOMOLOGICAL
DIMENSION
OF
ALGEBRAIC
CURVES
.
162
(10.3)
THE
GROUPS
H^X,
(G
RO
)X)
AND
F(X,(/Z
N
)
X
)
.
165
(10.4)
THE
FINITENESS
THEOREM
FOR
CONSTRUCTIBLE
SHEAVES
.
168
§11.
GENERAL
THEOREMS
IN
ETALE
COHOMOLOGY
THEORY
.
173
(11.1)
THE
COMPARISON
THEOREM
WITH
CLASSICAL
COHOMOLOGY
.
173
(11.2)
THE
COHOMOLOGICAL
DIMENSION
OF
ALGEBRAIC
SCHEMES
.
174
(11.3)
THE
BASE
CHANGE
THEOREM
FOR
PROPER
MORPHISMS
.
175
(11.4)
FINITENESS
THEOREMS
.
176
BIBLIOGRAPHY
.
179
INDEX
.
183 |
| any_adam_object | 1 |
| author | Tamme, Günter 1937-2022 |
| author_GND | (DE-588)117726052 |
| author_facet | Tamme, Günter 1937-2022 |
| author_role | aut |
| author_sort | Tamme, Günter 1937-2022 |
| author_variant | g t gt |
| building | Verbundindex |
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| callnumber-first | Q - Science |
| callnumber-label | QA564 |
| callnumber-raw | QA564 |
| callnumber-search | QA564 |
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 SK 300 SK 320 |
| ctrlnum | (OCoLC)30703628 (DE-599)BVBBV009770669 |
| dewey-full | 514/.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.23 |
| dewey-search | 514/.23 |
| dewey-sort | 3514 223 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV009770669 |
| illustrated | Not Illustrated |
| indexdate | 2024-08-16T01:34:30Z |
| institution | BVB |
| isbn | 0387571167 3540571167 9783540571162 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006464506 |
| oclc_num | 30703628 |
| open_access_boolean | |
| owner | DE-739 DE-355 DE-BY-UBR DE-703 DE-384 DE-29T DE-19 DE-BY-UBM DE-83 DE-11 DE-188 DE-706 |
| owner_facet | DE-739 DE-355 DE-BY-UBR DE-703 DE-384 DE-29T DE-19 DE-BY-UBM DE-83 DE-11 DE-188 DE-706 |
| physical | IX, 186 S. grap. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Tamme, Günter 1937-2022 Verfasser (DE-588)117726052 aut Einführung in die étale Kohomologie Introduction to étale cohomology Günter Tamme Berlin u.a. Springer 1994 IX, 186 S. grap. Darst. txt rdacontent n rdamedia nc rdacarrier Universitext Cohomologie gtt Faisceaux, théorie des ram Géométrie algébrique ram Homologie gtt Homologie ram Geometry, Algebraic Homology theory Sheaf theory Kohomologietheorie (DE-588)4164610-1 gnd rswk-swf Etalkohomologie (DE-588)4153071-8 gnd rswk-swf Etalkohomologie (DE-588)4153071-8 s DE-604 Kohomologietheorie (DE-588)4164610-1 s 1\p DE-604 Erscheint auch als Online-Ausgabe 978-3-642-78421-7 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006464506&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Tamme, Günter 1937-2022 Introduction to étale cohomology Cohomologie gtt Faisceaux, théorie des ram Géométrie algébrique ram Homologie gtt Homologie ram Geometry, Algebraic Homology theory Sheaf theory Kohomologietheorie (DE-588)4164610-1 gnd Etalkohomologie (DE-588)4153071-8 gnd |
| subject_GND | (DE-588)4164610-1 (DE-588)4153071-8 |
| title | Introduction to étale cohomology |
| title_alt | Einführung in die étale Kohomologie |
| title_auth | Introduction to étale cohomology |
| title_exact_search | Introduction to étale cohomology |
| title_full | Introduction to étale cohomology Günter Tamme |
| title_fullStr | Introduction to étale cohomology Günter Tamme |
| title_full_unstemmed | Introduction to étale cohomology Günter Tamme |
| title_short | Introduction to étale cohomology |
| title_sort | introduction to etale cohomology |
| topic | Cohomologie gtt Faisceaux, théorie des ram Géométrie algébrique ram Homologie gtt Homologie ram Geometry, Algebraic Homology theory Sheaf theory Kohomologietheorie (DE-588)4164610-1 gnd Etalkohomologie (DE-588)4153071-8 gnd |
| topic_facet | Cohomologie Faisceaux, théorie des Géométrie algébrique Homologie Geometry, Algebraic Homology theory Sheaf theory Kohomologietheorie Etalkohomologie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006464506&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT tammegunter einfuhrungindieetalekohomologie AT tammegunter introductiontoetalecohomology |