Cohomological theory of crystals over function fields:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Zürich
EMS
2009
|
| Schriftenreihe: | Tracts in mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 187 S. graph. Darst. |
| ISBN: | 9783037190746 |
Internformat
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV035875218 | ||
| 003 | DE-604 | ||
| 005 | 20130524 | ||
| 007 | t | ||
| 008 | 091209s2009 d||| |||| 00||| eng d | ||
| 020 | |a 9783037190746 |9 978-3-03719-074-6 | ||
| 035 | |a (OCoLC)471799851 | ||
| 035 | |a (DE-599)BVBBV035875218 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-355 |a DE-11 |a DE-91G |a DE-83 | ||
| 050 | 0 | |a QA612.3 | |
| 082 | 0 | |a 514/.23 |2 22 | |
| 084 | |a SK 780 |0 (DE-625)143255: |2 rvk | ||
| 084 | |a 18G60 |2 msc | ||
| 084 | |a MAT 122f |2 stub | ||
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| 084 | |a MAT 143f |2 stub | ||
| 084 | |a 11-02 |2 msc | ||
| 100 | 1 | |a Böckle, Gebhard |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Cohomological theory of crystals over function fields |c Gebhard Böckle ; Richard Pink |
| 264 | 1 | |a Zürich |b EMS |c 2009 | |
| 300 | |a VIII, 187 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Tracts in mathematics |v 9 | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Homology theory | |
| 650 | 4 | |a Number theory | |
| 650 | 0 | 7 | |a Kohomologietheorie |0 (DE-588)4164610-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a L-Funktion |0 (DE-588)4137026-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Kohomologietheorie |0 (DE-588)4164610-1 |D s |
| 689 | 0 | 1 | |a L-Funktion |0 (DE-588)4137026-0 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Pink, Richard |e Verfasser |4 aut | |
| 830 | 0 | |a Tracts in mathematics |v 9 |w (DE-604)BV022480257 |9 9 | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018732909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018732909 | ||
Datensatz im Suchindex
| _version_ | 1804140851707772928 |
|---|---|
| adam_text | Contents
Preface
.....................................
v
1
Introduction
1
2
Categorical preparations
13
2.1
Categories
................................ 13
2.2
Localization
............................... 17
2.3
Abelian categories
............................ 20
2.4
Grothendieck categories
........................ 23
2.5
Triangulated categories
......................... 26
2.6
Derived categories
........................... 27
2.7
Derived functors
............................ 30
2.8
Construction of derived functors
.................... 32
2.9
Comparison of derived categories
................... 36
3
Fundamental concepts
39
3.1
Conventions
............................... 39
3.2
τ
-sheaves
................................
40
3.3
Nilpotence
................................ 42
3.4
yl-crystals
................................ 47
3.5
Examples
................................ 49
4
Functors
52
4.1
Inverse image
.............................. 52
4.2
Tensor product
............................. 58
4.3
Change of coefficients
......................... 60
4.4
Direct image
............................... 61
4.5
Extension by zero
............................ 64
4.6
Constractibility
............................. 69
5
Derived categories
71
5.1
The
affine
case: ind-acyclic rfrj-modules
............... 71
5.2
Ind-acyclic
τ
-sheaves
..........................
76
5.3
Derived categories of
τ
-sheaves
and quasi-crystals
........... 81
5.4
Čech
resolution
...........................· · 84
6
Derived functors
88
6.1
Inverse image
.............................. 88
6.2
Tensor product
............................. 90
6.3
Change of coefficients
......................... 93
6.4
Direct image I
.............................. 93
6.5
Direct image II
............................. 97
viii Contents
6.6
Extension
by zero
............................ 99
6.7
Direct image with compact support
................... 101
7
Flatness
105
7.1
Flataess
of modules
........................... 105
7.2
Basic properties
............................. 107
7.3
Flataess
of the canonical representative
................ 109
7.4
Functoriality and constractibility
.................... 112
7.5
Representability
............................. 113
7.6
Complexes of finite Tor-dimension
................... 117
7.7
Regular coefficient rings
........................ 120
8
Naive ¿-functions
121
8.1
Basic properties
............................. 122
8.2
Duality
................................. 124
8.3
Anderson s trace formula
........................ 126
8.4
A cohomological trace formula
..................... 129
8.5
An extended example
.......................... 134
9
Crystalline ¿-functions
138
9.1
Characteristic polynomials
....................... 139
9.2
A primary decomposition for rational functions
............ 143
9.3
The local L-factor
............................ 145
9.4
The global ¿-function
.......................... 148
9.5
The ¿-function of a complex
...................... 150
9.6
Functoriality
............................... 151
9.7
Arbitrary coefficients
.......................... 157
9.8
Change of coefficients
......................... 160
10
Étale
cohomology
163
10.1
Basic Definitions
............................ 163
10.2
Functors
................................. 167
10.3
Equivalence of categories
........................ 169
10.4
Derived categories and functors
..................... 173
10.5
Flatness
................................. 173
10.6
¿-functions
............................... 174
Bibliography
177
List of notation
181
Index
185
|
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| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 780 |
| classification_tum | MAT 122f MAT 143f |
| ctrlnum | (OCoLC)471799851 (DE-599)BVBBV035875218 |
| 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.BV035875218 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:06:33Z |
| institution | BVB |
| isbn | 9783037190746 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018732909 |
| oclc_num | 471799851 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-11 DE-91G DE-BY-TUM DE-83 |
| physical | VIII, 187 S. graph. Darst. |
| publishDate | 2009 |
| publishDateSearch | 2009 |
| publishDateSort | 2009 |
| publisher | EMS |
| record_format | marc |
| series | Tracts in mathematics |
| series2 | Tracts in mathematics |
| spelling | Böckle, Gebhard Verfasser aut Cohomological theory of crystals over function fields Gebhard Böckle ; Richard Pink Zürich EMS 2009 VIII, 187 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Tracts in mathematics 9 Geometry, Algebraic Homology theory Number theory Kohomologietheorie (DE-588)4164610-1 gnd rswk-swf L-Funktion (DE-588)4137026-0 gnd rswk-swf Kohomologietheorie (DE-588)4164610-1 s L-Funktion (DE-588)4137026-0 s DE-604 Pink, Richard Verfasser aut Tracts in mathematics 9 (DE-604)BV022480257 9 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018732909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Böckle, Gebhard Pink, Richard Cohomological theory of crystals over function fields Tracts in mathematics Geometry, Algebraic Homology theory Number theory Kohomologietheorie (DE-588)4164610-1 gnd L-Funktion (DE-588)4137026-0 gnd |
| subject_GND | (DE-588)4164610-1 (DE-588)4137026-0 |
| title | Cohomological theory of crystals over function fields |
| title_auth | Cohomological theory of crystals over function fields |
| title_exact_search | Cohomological theory of crystals over function fields |
| title_full | Cohomological theory of crystals over function fields Gebhard Böckle ; Richard Pink |
| title_fullStr | Cohomological theory of crystals over function fields Gebhard Böckle ; Richard Pink |
| title_full_unstemmed | Cohomological theory of crystals over function fields Gebhard Böckle ; Richard Pink |
| title_short | Cohomological theory of crystals over function fields |
| title_sort | cohomological theory of crystals over function fields |
| topic | Geometry, Algebraic Homology theory Number theory Kohomologietheorie (DE-588)4164610-1 gnd L-Funktion (DE-588)4137026-0 gnd |
| topic_facet | Geometry, Algebraic Homology theory Number theory Kohomologietheorie L-Funktion |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018732909&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV022480257 |
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