Complex multiplication and lifting problems:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2014]
|
| Series: | Mathematical surveys and monographs
Volume 195 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | ix, 387 Seiten Illustrationen |
| ISBN: | 9781470410148 |
Staff View
MARC
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| 100 | 1 | |a Chai, Ching-Li |e Verfasser |0 (DE-588)112801862 |4 aut | |
| 245 | 1 | 0 | |a Complex multiplication and lifting problems |c Ching-Li Chai, Brian Conrad, Frans Oort |
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| 264 | 4 | |c © 2014 | |
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Record in the Search Index
| _version_ | 1804152032457654272 |
|---|---|
| adam_text | Contents
Preface
ix
Introduction
1
References
8
Notation
and terminology
9
Chapter
1.
Algebraic theory of complex multiplication
13
1.1.
Introduction
13
1.2.
Simplicity, isotypicity, and endomorphism algebras
15
1.3.
Complex multiplication
23
1.4.
Dieudonné
theory, />-divisible groups, and deformations
33
1.5.
CM types
65
1.6.
Abelian varieties over finite fields
70
1.7.
A theorem of Grothendieck and a construction of
Serre
76
1.8.
CM lifting questions
86
Chapter
2.
CM lifting over a discrete valuation ring
91
2.1.
Introduction
91
2.2.
Existence of CM lifting up to isogeny
102
2.3.
CM lifting to a normal domain up to isogeny: counterexamples
109
2.4.
Algebraic
Hecke
characters
117
2.5.
Theory of complex multiplication
127
2.6.
Local methods
130
Chapter
3.
CM lifting of p-divisible groups
137
3.1.
Motivation and background
137
3.2.
Properties of
α
-numbers
143
3.3. Isogenies
and duality
146
3.4.
Some p-divisible groups with small
α
-number
156
3.5.
Earlier non-liftability results and a new proof
161
3.6.
A lower bound on the field of definition
164
3.7.
Complex multiplication for ¿^divisible groups
166
3.8.
An upper bound for a field of definition
182
3.9.
Appendix: algebraic abelian p-adic representations of local fields
185
3.10.
Appendix: questions and examples on extending isogenies
191
Chapter
4.
CM lifting of abelian varieties up to isogeny
195
4.1.
Introduction
195
4.2.
Classification and Galois descent by Lie types
211
VII
viii CONTENTS
4.3.
Tensor
construction
for p-di visible groups
224
4.4.
Self-duality and CM lifting
228
4.5.
Striped and supersingular Lie types
233
4.6.
Complex conjugation and CM lifting
240
Appendix A. Some arithmetic results for abelian varieties
249
A.I. The p-part of Tate s work
249
A.
2,
The Main Theorem of Complex Multiplication
257
A.3. A converse to the Main Theorem of Complex Multiplication
292
A.
4.
Existence of algebraic
Hecke
characters
296
Appendix B. CM lifting via p-adic Hodge theory
321
B.I. A generalization of the toy model
321
B.2. Construct CM lifting by p-adic Hodge theory
333
B.3.
Dieudonné
theories over a perfect field of characteristic
ρ
343
В.
4.
p-adic Hodge theory and a formula for the closed fiber
359
Notes on Quotes
371
Glossary of Notations
373
Bibliography
379
Index
385
Abeìian
varieties with complex multipiication He
aí Lhe
origins of class Held theory,
and they play a central role in the contemporary theory of Shimura varieties. They
are special in characteristic
0
and ubiquitous over finite fields. This book explores the
relationship between such abelian varieties over finite fields and o ^r arithmetically
interesting fields of characteristic
0
via the study of several
naturai
CM lifting pn*bU ms
which had previously been solved only in special cases,
ín
addition to giving complete
solutions to such questions, the authors provide
numerou*
examples to
illustrate ine
generai
theory and present a detailed treatment of many fundamental results and
concepts in the arithmetic of
abeìian
varieties, such as the Mam Theorem of Complex,
Multiplication
and its generalizations, the finer aspects of
Tate
*s work on abelian vari¬
eties over
rinite
fields, and deformation theory.
ív
Iliis book
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|
| any_adam_object | 1 |
| author | Chai, Ching-Li Conrad, Brian 1970- Oort, Frans 1935- |
| author_GND | (DE-588)112801862 (DE-588)122429206 (DE-588)1065063040 |
| author_facet | Chai, Ching-Li Conrad, Brian 1970- Oort, Frans 1935- |
| author_role | aut aut aut |
| author_sort | Chai, Ching-Li |
| author_variant | c l c clc b c bc f o fo |
| building | Verbundindex |
| bvnumber | BV041738284 |
| classification_rvk | SK 240 |
| classification_tum | MAT 147f |
| ctrlnum | (OCoLC)870208141 (DE-599)BSZ400225921 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV041738284 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:04:09Z |
| institution | BVB |
| isbn | 9781470410148 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027184930 |
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| physical | ix, 387 Seiten Illustrationen |
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| publisher | American Mathematical Society |
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| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spelling | Chai, Ching-Li Verfasser (DE-588)112801862 aut Complex multiplication and lifting problems Ching-Li Chai, Brian Conrad, Frans Oort Providence, Rhode Island American Mathematical Society [2014] © 2014 ix, 387 Seiten Illustrationen txt rdacontent n rdamedia nc rdacarrier Mathematical surveys and monographs Volume 195 Komplexe Multiplikation (DE-588)4164903-5 gnd rswk-swf Liften Mathematik (DE-588)4167655-5 gnd rswk-swf Komplexe Multiplikation (DE-588)4164903-5 s Liften Mathematik (DE-588)4167655-5 s DE-604 Conrad, Brian 1970- Verfasser (DE-588)122429206 aut Oort, Frans 1935- Verfasser (DE-588)1065063040 aut Erscheint auch als Online-Ausgabe 978-1-4704-1474-0 Mathematical surveys and monographs Volume 195 (DE-604)BV000018014 195 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027184930&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027184930&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Chai, Ching-Li Conrad, Brian 1970- Oort, Frans 1935- Complex multiplication and lifting problems Mathematical surveys and monographs Komplexe Multiplikation (DE-588)4164903-5 gnd Liften Mathematik (DE-588)4167655-5 gnd |
| subject_GND | (DE-588)4164903-5 (DE-588)4167655-5 |
| title | Complex multiplication and lifting problems |
| title_auth | Complex multiplication and lifting problems |
| title_exact_search | Complex multiplication and lifting problems |
| title_full | Complex multiplication and lifting problems Ching-Li Chai, Brian Conrad, Frans Oort |
| title_fullStr | Complex multiplication and lifting problems Ching-Li Chai, Brian Conrad, Frans Oort |
| title_full_unstemmed | Complex multiplication and lifting problems Ching-Li Chai, Brian Conrad, Frans Oort |
| title_short | Complex multiplication and lifting problems |
| title_sort | complex multiplication and lifting problems |
| topic | Komplexe Multiplikation (DE-588)4164903-5 gnd Liften Mathematik (DE-588)4167655-5 gnd |
| topic_facet | Komplexe Multiplikation Liften Mathematik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027184930&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027184930&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
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