Topological automorphic forms:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I.
American Math. Soc.
2010
|
| Series: | Memoirs of the American Mathematical Society
958 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Volume 204, number 958 (second of 5 numbers) Literaturverz.: S. 129 - 132 |
| Physical Description: | XXIII, 136 S. graph. Darst. |
| ISBN: | 9780821845394 |
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MARC
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| 100 | 1 | |a Behrens, Mark |d 1975- |e Verfasser |0 (DE-588)140795200 |4 aut | |
| 245 | 1 | 0 | |a Topological automorphic forms |c Mark Behrens, Tyler Lawson |
| 264 | 1 | |a Providence, R.I. |b American Math. Soc. |c 2010 | |
| 300 | |a XXIII, 136 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society |v 958 | |
| 500 | |a Volume 204, number 958 (second of 5 numbers) | ||
| 500 | |a Literaturverz.: S. 129 - 132 | ||
| 650 | 4 | |a Automorphic forms | |
| 650 | 4 | |a Algebraic topology | |
| 650 | 4 | |a Homotopy groups | |
| 650 | 4 | |a Shimura varieties | |
| 650 | 0 | 7 | |a Algebraische Topologie |0 (DE-588)4120861-4 |2 gnd |9 rswk-swf |
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Record in the Search Index
| _version_ | 1804141144318148608 |
|---|---|
| adam_text | 3.2.
Virtual subgroups and quasi-isogenies
3.3.
Level structures
3.4.
The
Tate
representation
3.5.
Homomorphisms of abelian schemes
Chapter
4.
Polarizations
4.1.
Polarizations
4.2.
The
Rosati
involution
4.3.
The Weil pairing
4.4.
Polarizations of B-linear abelian varieties
4.5.
Induced polarizations
4.6.
Classification of weak polarizations
Contents
Introduction yji
0.1.
Background
and motivation
vii
0.2.
Subject matter of this book xv
0.3.
Organization of this book
xxi
0.4.
Acknowledgments xxjjj
Chapter
1.
p-divisible groups
1.1.
Definitions
1
1.2.
Classification
3
Chapter
2.
The Honda-Tate classification
5
2.1.
Abelian varieties over finite fields
5
2.2.
Abelian varieties over Fp
б
Chapter
3.
Tate
modules and level structures
13
3.1.
Tate
modules of abelian varieties
13
14
15
15
16
19
19
22
22
23
23
24
Chapter
5.
Forms and involutions
27
5.1.
Hermitian forms
27
5.2.
Unitary and similitude groups
30
5.3.
Classification of forms
31
Chapter
6.
Shimura varieties of type
(7(1,
η
- 1) 35
6.1.
Motivation
35
6.2.
Initial data
36
6.3.
Statement of the moduli problem
37
6.4.
Equivalence of the moduli problems
39
6.5.
Moduli problems with level structure
41
6.6.
Shimura stacks
42
iv
CONTENTS
Chapter
7.
Deformation theory
45
7.1.
Deformations of ^divisible groups
45
7.2.
Serre-Tate
theory
47
7.3.
Deformation theory of points of Sh
47
Chapter
8.
Topological automorphic forms
51
8.1.
The generalized Hopkins-Miller theorem
51
8.2.
The descent spectral sequence
54
8.3.
Application to Shimura stacks
56
Chapter
9.
Relationship to automorphic forms
57
9.1.
Alternate description of Sh{Kp)
57
9.2.
Description of Sh(KP)F
59
9.3.
Description of Sh(Kp)c
59
9.4.
Automorphic forms
62
Chapter
10.
Smooth G-spectra
65
10.1.
Smooth G-sets
65
10.2.
The category of simplicial smooth G-sets
67
10.3.
The category of smooth G-spectra
69
10.4.
Smooth homotopy fixed points
70
10.5.
Restriction, induction, and coinduction
71
10.6.
Descent from compact open subgroups
72
10.7.
Transfer maps and the Burnside category
74
Chapter
11.
Operations on
TAF
79
11.1.
The ^co-action of
Gf/fA? 00)
79
11.2. Hecke
operators
80
Chapter
12.
Buildings
87
12.1.
Terminology
87
12.2.
The buildings for GL and SL
88
12.3.
The buildings for
U
and GU
89
Chapter
13.
Hypercohomology of
adele
groups
95
13.1.
Definition of Qou and Qu
95
13.2.
The semi-cosimplicial resolution
95
Chapter
14.
К
(n)-local theory
103
14.1.
Endomorphisms of mod
ρ
points
103
14.2.
Approximation results
105
14.3.
The height
η
locus of Sh(Kp)
108
14.4.
К
(n)-local
TAF
113
14.5.
Kinj-localQu
118
Chapter
15.
Example: chromatic level
1 121
15.1.
Unit groups and the if(l)-local sphere
121
15.2.
Topological automorphic forms in chromatic filtration
1 123
Bibliography
129
Index
133
|
| any_adam_object | 1 |
| author | Behrens, Mark 1975- Lawson, Tyler 1977- |
| author_GND | (DE-588)140795200 (DE-588)140795219 |
| author_facet | Behrens, Mark 1975- Lawson, Tyler 1977- |
| author_role | aut aut |
| author_sort | Behrens, Mark 1975- |
| author_variant | m b mb t l tl |
| building | Verbundindex |
| bvnumber | BV036084675 |
| callnumber-first | Q - Science |
| callnumber-label | QA353 |
| callnumber-raw | QA353.A9 |
| callnumber-search | QA353.A9 |
| callnumber-sort | QA 3353 A9 |
| callnumber-subject | QA - Mathematics |
| ctrlnum | (OCoLC)489257121 (DE-599)BVBBV036084675 |
| dewey-full | 515/.9 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515/.9 |
| dewey-search | 515/.9 |
| dewey-sort | 3515 19 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV036084675 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:11:12Z |
| institution | BVB |
| isbn | 9780821845394 |
| language | English |
| lccn | 2009049931 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018975660 |
| oclc_num | 489257121 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-29T DE-83 |
| owner_facet | DE-355 DE-BY-UBR DE-29T DE-83 |
| physical | XXIII, 136 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | American Math. Soc. |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Behrens, Mark 1975- Verfasser (DE-588)140795200 aut Topological automorphic forms Mark Behrens, Tyler Lawson Providence, R.I. American Math. Soc. 2010 XXIII, 136 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society 958 Volume 204, number 958 (second of 5 numbers) Literaturverz.: S. 129 - 132 Automorphic forms Algebraic topology Homotopy groups Shimura varieties Algebraische Topologie (DE-588)4120861-4 gnd rswk-swf Automorphe Form (DE-588)4003972-9 gnd rswk-swf Fundamentalgruppe (DE-588)4155638-0 gnd rswk-swf Automorphe Form (DE-588)4003972-9 s Algebraische Topologie (DE-588)4120861-4 s Fundamentalgruppe (DE-588)4155638-0 s DE-604 Lawson, Tyler 1977- Verfasser (DE-588)140795219 aut Memoirs of the American Mathematical Society 958 (DE-604)BV008000141 958 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018975660&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Behrens, Mark 1975- Lawson, Tyler 1977- Topological automorphic forms Memoirs of the American Mathematical Society Automorphic forms Algebraic topology Homotopy groups Shimura varieties Algebraische Topologie (DE-588)4120861-4 gnd Automorphe Form (DE-588)4003972-9 gnd Fundamentalgruppe (DE-588)4155638-0 gnd |
| subject_GND | (DE-588)4120861-4 (DE-588)4003972-9 (DE-588)4155638-0 |
| title | Topological automorphic forms |
| title_auth | Topological automorphic forms |
| title_exact_search | Topological automorphic forms |
| title_full | Topological automorphic forms Mark Behrens, Tyler Lawson |
| title_fullStr | Topological automorphic forms Mark Behrens, Tyler Lawson |
| title_full_unstemmed | Topological automorphic forms Mark Behrens, Tyler Lawson |
| title_short | Topological automorphic forms |
| title_sort | topological automorphic forms |
| topic | Automorphic forms Algebraic topology Homotopy groups Shimura varieties Algebraische Topologie (DE-588)4120861-4 gnd Automorphe Form (DE-588)4003972-9 gnd Fundamentalgruppe (DE-588)4155638-0 gnd |
| topic_facet | Automorphic forms Algebraic topology Homotopy groups Shimura varieties Algebraische Topologie Automorphe Form Fundamentalgruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018975660&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT behrensmark topologicalautomorphicforms AT lawsontyler topologicalautomorphicforms |