Complex multiplication:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
1983
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften
255 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 184 S. |
| ISBN: | 3540907866 9780387907864 0387907866 |
Internformat
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| 100 | 1 | |a Lang, Serge |d 1927-2005 |e Verfasser |0 (DE-588)119305119 |4 aut | |
| 245 | 1 | 0 | |a Complex multiplication |c Serge Lang |
| 264 | 1 | |a New York [u.a.] |b Springer |c 1983 | |
| 300 | |a VIII, 184 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Grundlehren der mathematischen Wissenschaften |v 255 | |
| 650 | 7 | |a Complexe getallen |2 gtt | |
| 650 | 4 | |a Multiplication complexe | |
| 650 | 7 | |a Multiplication complexe |2 ram | |
| 650 | 7 | |a Vermenigvuldiging |2 gtt | |
| 650 | 4 | |a Multiplication, Complex | |
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Datensatz im Suchindex
| _version_ | 1804114628812210176 |
|---|---|
| adam_text | Contents
CHAPTER
1
Analytic Complex Multiplication
.................. 1
1.
Positive Definite Involutions
..................... 4
2.
CM Types and Subfields
....................... 6
3.
Application to Abelian Manifolds
................... 8
4.
Construction of Abelian Manifolds with CM
.............. 14
5.
Reflex of a CM Type
........................ 21
6.
Application to Cyclotomic Fields
................... 24
7.
An Example: The
Fermat
Curve
................... 29
CHAPTER
2
Some Algebraic Properties of Abelian Varieties
........... 35
1
.
Invariant Differential Forms
..................... 35
2.
Homomorphisms and Inseparability
.................. 40
3.
Reduction mod
ρ
and
/-adic
Representations
.............. 43
4.
Reduction of Functions
........................ 50
5.
Reduction of Differential Forms
................... 51
CHAPTER
3
Algebraic Complex Multiplication
................. 53
1.
Fields of Definition
......................... 53
2.
Transformations and Multiplications
................. 55
3.
The Congruence Relation
...................... 61
4.
Polarizations
...................... ...... 67
5.
Change of Riemann Forms Under Various Maps
............ 73
6.
The Main Theorem of Complex Multiplication
............. 76
CHAPTER
4
The CM Character
......................... 84
1.
The Second Main Theorem of Complex Multiplication
and the CM Character
........................ 84
2.
Finite Extensions
.......................... 94
viii Contents
3.
Algebraic Properties of the Associated Characters
............ 102
4.
The CM Character over a Quadratic Subfield
.............. 106
5.
Shimura s l-adic Representations
................... 110
6.
Application to the
Zeta
Function in the CM Case
............ 115
CHAPTER
5
Fields of Moduli,
Kummer
Varieties, and Descents
......... 122
1.
Fields of Moduli
.......................... 122
2.
General Descent
.......................... 130
3. Kummer
Varieties
......................... 132
4.
Class Fields as Moduli Fields
..................... 136
5.
Casselman s Theorem
..............
%
.......... 139
6.
Descent to a Quadratic Subfield
.................... 142
7.
Further Descent Theorems
...................... 145
CHAPTER
6
The Type Norm
........................... 148
1.
The Rank of a Type
......................... 148
2.
The Type Norm as Lie Homomorphism
................ 152
3.
The Image
Νφ(ο*)
......................... 155
4.
The Type Norm as Algebraic Homomorphism
............. 156
5.
Application to Abelian Varieties
................... 160
CHAPTER
7
Arbitrary Conjugations of CM Types
................ 163
1.
The Reflex Norm and the Type Transfer
................ 163
2.
General Reciprocity and the Type Transfer
............... 167
3.
Application to the Conjugation of Abelian Varieties
........... 170
4.
Another Property Implying
еф
=1.................. 75
Bibliography
............................ 79
Index
................................ 183
|
| any_adam_object | 1 |
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| author_facet | Lang, Serge 1927-2005 |
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| bvnumber | BV000169522 |
| callnumber-first | Q - Science |
| callnumber-label | QA564 |
| callnumber-raw | QA564 |
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| ctrlnum | (OCoLC)9934103 (DE-599)BVBBV000169522 |
| dewey-full | 512/.33 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.33 |
| dewey-search | 512/.33 |
| dewey-sort | 3512 233 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV000169522 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:09:45Z |
| institution | BVB |
| isbn | 3540907866 9780387907864 0387907866 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000096528 |
| oclc_num | 9934103 |
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| owner | DE-12 DE-384 DE-703 DE-154 DE-739 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-634 DE-188 |
| owner_facet | DE-12 DE-384 DE-703 DE-154 DE-739 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-634 DE-188 |
| physical | VIII, 184 S. |
| publishDate | 1983 |
| publishDateSearch | 1983 |
| publishDateSort | 1983 |
| publisher | Springer |
| record_format | marc |
| series | Grundlehren der mathematischen Wissenschaften |
| series2 | Grundlehren der mathematischen Wissenschaften |
| spelling | Lang, Serge 1927-2005 Verfasser (DE-588)119305119 aut Complex multiplication Serge Lang New York [u.a.] Springer 1983 VIII, 184 S. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 255 Complexe getallen gtt Multiplication complexe Multiplication complexe ram Vermenigvuldiging gtt Multiplication, Complex Abelsche Gruppe (DE-588)4140988-7 gnd rswk-swf Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Komplexe Multiplikation (DE-588)4164903-5 gnd rswk-swf Komplexe Multiplikation (DE-588)4164903-5 s DE-604 Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Abelsche Gruppe (DE-588)4140988-7 s Komplexe Mannigfaltigkeit (DE-588)4031996-9 s Grundlehren der mathematischen Wissenschaften 255 (DE-604)BV000000395 255 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000096528&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Lang, Serge 1927-2005 Complex multiplication Grundlehren der mathematischen Wissenschaften Complexe getallen gtt Multiplication complexe Multiplication complexe ram Vermenigvuldiging gtt Multiplication, Complex Abelsche Gruppe (DE-588)4140988-7 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd |
| subject_GND | (DE-588)4140988-7 (DE-588)4031996-9 (DE-588)4140992-9 (DE-588)4164903-5 |
| title | Complex multiplication |
| title_auth | Complex multiplication |
| title_exact_search | Complex multiplication |
| title_full | Complex multiplication Serge Lang |
| title_fullStr | Complex multiplication Serge Lang |
| title_full_unstemmed | Complex multiplication Serge Lang |
| title_short | Complex multiplication |
| title_sort | complex multiplication |
| topic | Complexe getallen gtt Multiplication complexe Multiplication complexe ram Vermenigvuldiging gtt Multiplication, Complex Abelsche Gruppe (DE-588)4140988-7 gnd Komplexe Mannigfaltigkeit (DE-588)4031996-9 gnd Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Komplexe Multiplikation (DE-588)4164903-5 gnd |
| topic_facet | Complexe getallen Multiplication complexe Vermenigvuldiging Multiplication, Complex Abelsche Gruppe Komplexe Mannigfaltigkeit Abelsche Mannigfaltigkeit Komplexe Multiplikation |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000096528&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000395 |
| work_keys_str_mv | AT langserge complexmultiplication |