Compactifying moduli spaces for abelian varieties:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2008
|
| Schriftenreihe: | Lecture notes in mathematics
1958 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VI, 278 S. graph. Darst. |
| ISBN: | 9783540705185 9783540705192 |
Internformat
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| 100 | 1 | |a Olsson, Martin C. |d ca. 20./21. Jh. |e Verfasser |0 (DE-588)136161952 |4 aut | |
| 245 | 1 | 0 | |a Compactifying moduli spaces for abelian varieties |c Martin C. Olsson |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a VI, 278 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 1958 | |
| 650 | 4 | |a Théorie des modules | |
| 650 | 4 | |a Variétés abéliennes | |
| 650 | 4 | |a Abelian varieties | |
| 650 | 4 | |a Moduli theory | |
| 650 | 0 | 7 | |a Abelsche Mannigfaltigkeit |0 (DE-588)4140992-9 |2 gnd |9 rswk-swf |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-016703302 | ||
Datensatz im Suchindex
| _version_ | 1804137966194393088 |
|---|---|
| adam_text | Contents
Summary
......................................................
VII
0
Introduction
............................................... 1
1
A Brief Primer on Algebraic Stacks
....................... 7
1.1
S-groupoids
............................................ 7
1.2
Stacks
................................................. 17
1.3
Comparison of Topologies
................................ 25
1.4
Coarse Moduli Spaces
.................................... 26
1.5
Rigidification of Stacks
................................... 26
2
Preliminaries
.............................................. 31
2.1
Abelian Schemes and
Torsors
............................. 31
2.2
Biextensions
............................................ 34
2.3
Logarithmic Geometry
................................... 43
2.4
Summary of Alexeev s Results
............................ 51
3
Moduli of Broken Toric Varieties
.......................... 57
3.1
The Basic Construction
.................................. 57
3.2
Automorphisms of the Standard Family over a Field
......... 67
3.3
Deformation Theory
..................................... 70
3.4
Algebraization
.......................................... 75
3.5
Approximation
.......................................... 76
3.6
Automorphisms over a General Base
....................... 78
3.7
The Stack
JťQ
.......................................... 80
4
Moduli of Principally Polarized Abelian Varieties
.......... 85
4.1
The Standard Construction
............................... 85
4.2
Automorphisms over a Field
.............................. 93
4.3
Deformation Theory
..................................... 98
4.4
Isomorphisms over Artinian Local Rings
....................110
VI
Contents
4.5 Versal
Families
..........................................
ИЗ
4.6
Definition of the Moduli Problem
..........................121
4.7
The Valuative Criterion for Properness
.....................121
4.8
Algebraization
..........................................125
4.9
Completion of Proof of
4.6.2..............................130
5
Moduli of Abelian Varieties with Higher Degree
Polarizations
..............................................135
5.1
Rethinking
stfg¿
.........................................135
5.2
The Standard Construction^
..............................138
5.3
Another Interpretation of
&> -» & ........................142
5.4
The Theta Group
.......................................144
5.5
Deformation Theory
.....................................158
5.6
Isomorphisms without Log Structures
......................160
5.7
Algebraization of Formal Log Structures
....................163
5.8
Description of the Group
Я|р
.............................166
5.9
Specialization
...........................................178
5.10
Isomorphisms in ¿?g,d
....................................201
5.11
Rigidification
...... .....................................202
5.12
Example: Higher Dimensional
Tate
Curve
..................207
5.13
The Case g = l
.........................................225
6
Level Structure
............................................231
6.1
First Approach Using
Kummer
étale
Topology
..............231
6.2
Second Approach using the Theta Group
...................237
6.3
Resolving Singularities of Theta Functions
..................241
References
.....................................................273
Index of Terminology
..........................................277
Index of Notation
.............................................279
|
| adam_txt |
Contents
Summary
.
VII
0
Introduction
. 1
1
A Brief Primer on Algebraic Stacks
. 7
1.1
S-groupoids
. 7
1.2
Stacks
. 17
1.3
Comparison of Topologies
. 25
1.4
Coarse Moduli Spaces
. 26
1.5
Rigidification of Stacks
. 26
2
Preliminaries
. 31
2.1
Abelian Schemes and
Torsors
. 31
2.2
Biextensions
. 34
2.3
Logarithmic Geometry
. 43
2.4
Summary of Alexeev's Results
. 51
3
Moduli of Broken Toric Varieties
. 57
3.1
The Basic Construction
. 57
3.2
Automorphisms of the Standard Family over a Field
. 67
3.3
Deformation Theory
. 70
3.4
Algebraization
. 75
3.5
Approximation
. 76
3.6
Automorphisms over a General Base
. 78
3.7
The Stack
JťQ
. 80
4
Moduli of Principally Polarized Abelian Varieties
. 85
4.1
The Standard Construction
. 85
4.2
Automorphisms over a Field
. 93
4.3
Deformation Theory
. 98
4.4
Isomorphisms over Artinian Local Rings
.110
VI
Contents
4.5 Versal
Families
.
ИЗ
4.6
Definition of the Moduli Problem
.121
4.7
The Valuative Criterion for Properness
.121
4.8
Algebraization
.125
4.9
Completion of Proof of
4.6.2.130
5
Moduli of Abelian Varieties with Higher Degree
Polarizations
.135
5.1
Rethinking
stfg¿
.135
5.2
The Standard Construction^
.138
5.3
Another Interpretation of
&> -» & .142
5.4
The Theta Group
.144
5.5
Deformation Theory
.158
5.6
Isomorphisms without Log Structures
.160
5.7
Algebraization of Formal Log Structures
.163
5.8
Description of the Group
Я|р
.166
5.9
Specialization
.178
5.10
Isomorphisms in ¿?g,d
.201
5.11
Rigidification
.'.202
5.12
Example: Higher Dimensional
Tate
Curve
.207
5.13
The Case g = l
.225
6
Level Structure
.231
6.1
First Approach Using
Kummer
étale
Topology
.231
6.2
Second Approach using the Theta Group
.237
6.3
Resolving Singularities of Theta Functions
.241
References
.273
Index of Terminology
.277
Index of Notation
.279 |
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| author | Olsson, Martin C. ca. 20./21. Jh |
| author_GND | (DE-588)136161952 |
| author_facet | Olsson, Martin C. ca. 20./21. Jh |
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| classification_tum | MAT 147f |
| ctrlnum | (OCoLC)232976387 (DE-599)BSZ285357085 |
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| discipline | Mathematik |
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| illustrated | Illustrated |
| index_date | 2024-07-02T21:51:00Z |
| indexdate | 2024-07-09T21:20:41Z |
| institution | BVB |
| isbn | 9783540705185 9783540705192 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016703302 |
| oclc_num | 232976387 |
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| physical | VI, 278 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
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| publisher | Springer |
| record_format | marc |
| series | Lecture notes in mathematics |
| series2 | Lecture notes in mathematics |
| spelling | Olsson, Martin C. ca. 20./21. Jh. Verfasser (DE-588)136161952 aut Compactifying moduli spaces for abelian varieties Martin C. Olsson Berlin [u.a.] Springer 2008 VI, 278 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 1958 Théorie des modules Variétés abéliennes Abelian varieties Moduli theory Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd rswk-swf Kompaktifizierung (DE-588)4164859-6 gnd rswk-swf Modulraum (DE-588)4183462-8 gnd rswk-swf Abelsche Mannigfaltigkeit (DE-588)4140992-9 s Modulraum (DE-588)4183462-8 s Kompaktifizierung (DE-588)4164859-6 s DE-604 Lecture notes in mathematics 1958 (DE-604)BV000676446 1958 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016703302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Olsson, Martin C. ca. 20./21. Jh Compactifying moduli spaces for abelian varieties Lecture notes in mathematics Théorie des modules Variétés abéliennes Abelian varieties Moduli theory Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Kompaktifizierung (DE-588)4164859-6 gnd Modulraum (DE-588)4183462-8 gnd |
| subject_GND | (DE-588)4140992-9 (DE-588)4164859-6 (DE-588)4183462-8 |
| title | Compactifying moduli spaces for abelian varieties |
| title_auth | Compactifying moduli spaces for abelian varieties |
| title_exact_search | Compactifying moduli spaces for abelian varieties |
| title_exact_search_txtP | Compactifying moduli spaces for abelian varieties |
| title_full | Compactifying moduli spaces for abelian varieties Martin C. Olsson |
| title_fullStr | Compactifying moduli spaces for abelian varieties Martin C. Olsson |
| title_full_unstemmed | Compactifying moduli spaces for abelian varieties Martin C. Olsson |
| title_short | Compactifying moduli spaces for abelian varieties |
| title_sort | compactifying moduli spaces for abelian varieties |
| topic | Théorie des modules Variétés abéliennes Abelian varieties Moduli theory Abelsche Mannigfaltigkeit (DE-588)4140992-9 gnd Kompaktifizierung (DE-588)4164859-6 gnd Modulraum (DE-588)4183462-8 gnd |
| topic_facet | Théorie des modules Variétés abéliennes Abelian varieties Moduli theory Abelsche Mannigfaltigkeit Kompaktifizierung Modulraum |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016703302&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
| work_keys_str_mv | AT olssonmartinc compactifyingmodulispacesforabelianvarieties |