Néron models:
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin
Springer-Verlag
1990
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
Folge 3 ; 21 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Literaturverzeichnis: Seite 317 - 321 |
| Physical Description: | X, 325 Seiten Diagramme |
| ISBN: | 3540505873 9783642080739 0387505873 |
Staff View
MARC
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| 020 | |a 9783642080739 |c softcover |9 978-3-642-08073-9 | ||
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| 100 | 1 | |a Bosch, Siegfried |d 1944- |e Verfasser |0 (DE-588)106950827 |4 aut | |
| 245 | 1 | 0 | |a Néron models |c Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud |
| 264 | 1 | |a Berlin |b Springer-Verlag |c 1990 | |
| 300 | |a X, 325 Seiten |b Diagramme | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 |v 21 | |
| 500 | |a Literaturverzeichnis: Seite 317 - 321 | ||
| 650 | 7 | |a Néron, Modèles de |2 ram | |
| 650 | 4 | |a Variétés abéliennes | |
| 650 | 7 | |a Variétés abéliennes |2 ram | |
| 650 | 0 | 7 | |a Varietät |g Mathematik |0 (DE-588)4325475-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Néron-Modell |0 (DE-588)4233203-5 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |2 gnd |9 rswk-swf |
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| 689 | 1 | 0 | |a Algebraische Geometrie |0 (DE-588)4001161-6 |D s |
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| 700 | 1 | |a Raynaud, Michel |d 1938- |e Verfasser |0 (DE-588)1045403911 |4 aut | |
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Record in the Search Index
| _version_ | 1804117049097584640 |
|---|---|
| adam_text | Table
of
Contents
Introduction
.................................................... 1
Chapter
1.
What Is
a Néron
Model?
................................ 6
1.1
Integral Points
............................................... 6
1.2
Néron
Models
............................................... 12
1.3
The Local Case: Main Existence Theorem
....................... 16
1.4
The Global Case: Abelian Varieties
............................. 18
1.5
Elliptic Curves
............................................... 20
1.6
Néron s
Original Article
....................................... 27
Chapter
2.
Some Background Material from Algebraic Geometry
....... 31
2.1
Differential Forms
........................................... 31
2.2
Smoothness
................................................. 34
2.3
Henselian Rings
............................................. 44
2.4
Flatness
.................................................... 51
2.5
S-Rationai Maps
............................................. 55
Chapter
3.
The Smoothening Process
............................... 60
3.1
Statement of the Theorem
..................................... 60
3.2
Dilatation
.................................................. 62
3.3
Néron s
Measure for the Defect of Smoothness
................... 64
3.4
Proof of the Theorem
.......................................... 71
3.5
Weak
Néron
Models
......................................... 73
3.6
Algebraic Approximation of Formal Points
.......,.............. 77
Chapter
4.
Construction of
Birational
Group Laws
................... 94
4.1
Group Schemes
.............................................. 94
4.2
Invariant Differential Forms
................................... 99
4.3 Ä-Extensions
of
Х
-Group Laws
................................ 103
4.4
Rational Maps into Group Schemes
............................ 109
Chapter
5.
From
Birational
Group Laws to Group Schemes
............ 112
5.1
Statement of the Theorem
.................................----- 112
5.2
Strict
Birational
Group Laws
.................................. 114
5.3
Proof of the Theorem for a Strictly Henselian Base
................ 119
χ
Table of
Contents
Chapter
6.
Descent
............................................... 129
6.1
The General Problem
......................................... 129
6.2
Some Standard Examples of Descent
............................ 138
6.3
The Theorem of the Square
.................................... 148
6.4
The Quasi-Projectivity of
Torsors
............................... 152
6.5
The Descent of
Torsors
....................................... 156
6.6
Applications to
Birational
Group Laws
.......................... 162
6.7
An Example of Non-Effective Descent
.......................... 166
Chapter
7.
Properties of
Néron
Models
............................. 172
7.1
A Criterion
................................................. 172
7.2
Base Change and Descent
..................................... 176
7.3 Isogenies................................................... 178
7.4
Semi-Abelian Reduction
...................................... 181
7.5
Exactness Properties
.......................................... 184
7.6
Weil Restriction
............................................. 191
Chapter
8.
The
Picard
Functor
.................................... 199
8.1
Basics on the Relative
Picard
Functor
........................... 199
8.2
Representability by a Scheme
.................................. 209
8.3
Representability by an Algebraic Space
.......................... 223
8.4
Properties
................................................... 231
Chapter
9.
Jacobians of Relative Curves
............................. 236
9.1
The Degree of Divisors
....................................... 236
9.2
The Structure of Jacobians
.................................... 243
9.3
Construction via
Birational
Group Laws
........................ 251
9.4
Construction via Algebraic Spaces
.............................. 259
9.5
Picard
Functor and
Néron
Models of Jacobians
.................. 264
9.6
The Group of Connected Components of
a Néron
Model
.......... 273
9.7
Rational Singularities
......................................... 286
Chapter
10.
Néron
Models of Not Necessarily Proper Algebraic Groups
.. 289
10.1
Generalities
................................................ 289
10.2
The Local Case
............................................. 296
10.3
The Global Case
............................................ 309
Bibliography
.................................................... 317
Subject Index
.................................................... 322
|
| any_adam_object | 1 |
| author | Bosch, Siegfried 1944- Lütkebohmert, Werner Raynaud, Michel 1938- |
| author_GND | (DE-588)106950827 (DE-588)124615163 (DE-588)1045403911 |
| author_facet | Bosch, Siegfried 1944- Lütkebohmert, Werner Raynaud, Michel 1938- |
| author_role | aut aut aut |
| author_sort | Bosch, Siegfried 1944- |
| author_variant | s b sb w l wl m r mr |
| building | Verbundindex |
| bvnumber | BV002675462 |
| callnumber-first | Q - Science |
| callnumber-label | QA564B587 1990 |
| callnumber-raw | QA564B587 1990 |
| callnumber-search | QA564B587 1990 |
| callnumber-sort | QA 3564 B587 41990 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 240 SK 320 |
| classification_tum | MAT 147f |
| ctrlnum | (OCoLC)423257454 (DE-599)BVBBV002675462 |
| dewey-full | 516.35 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.35 |
| dewey-search | 516.35 |
| dewey-sort | 3516.35 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV002675462 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:48:13Z |
| institution | BVB |
| isbn | 3540505873 9783642080739 0387505873 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-001715001 |
| oclc_num | 423257454 |
| open_access_boolean | |
| owner | DE-12 DE-384 DE-91 DE-BY-TUM DE-703 DE-739 DE-355 DE-BY-UBR DE-20 DE-824 DE-29T DE-19 DE-BY-UBM DE-706 DE-83 DE-11 |
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| physical | X, 325 Seiten Diagramme |
| psigel | TUB-nve |
| publishDate | 1990 |
| publishDateSearch | 1990 |
| publishDateSort | 1990 |
| publisher | Springer-Verlag |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 |
| spelling | Bosch, Siegfried 1944- Verfasser (DE-588)106950827 aut Néron models Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud Berlin Springer-Verlag 1990 X, 325 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : Folge 3 21 Literaturverzeichnis: Seite 317 - 321 Néron, Modèles de ram Variétés abéliennes Variétés abéliennes ram Varietät Mathematik (DE-588)4325475-5 gnd rswk-swf Néron-Modell (DE-588)4233203-5 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Néron-Modell (DE-588)4233203-5 s DE-604 Algebraische Geometrie (DE-588)4001161-6 s Varietät Mathematik (DE-588)4325475-5 s Lütkebohmert, Werner Verfasser (DE-588)124615163 aut Raynaud, Michel 1938- Verfasser (DE-588)1045403911 aut Erscheint auch als Online-Ausgabe, PDF 978-3-642-51438-8 Ergebnisse der Mathematik und ihrer Grenzgebiete Folge 3 ; 21 (DE-604)BV000899194 21 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001715001&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bosch, Siegfried 1944- Lütkebohmert, Werner Raynaud, Michel 1938- Néron models Ergebnisse der Mathematik und ihrer Grenzgebiete Néron, Modèles de ram Variétés abéliennes Variétés abéliennes ram Varietät Mathematik (DE-588)4325475-5 gnd Néron-Modell (DE-588)4233203-5 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4325475-5 (DE-588)4233203-5 (DE-588)4001161-6 |
| title | Néron models |
| title_auth | Néron models |
| title_exact_search | Néron models |
| title_full | Néron models Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud |
| title_fullStr | Néron models Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud |
| title_full_unstemmed | Néron models Siegfried Bosch, Werner Lütkebohmert, Michel Raynaud |
| title_short | Néron models |
| title_sort | neron models |
| topic | Néron, Modèles de ram Variétés abéliennes Variétés abéliennes ram Varietät Mathematik (DE-588)4325475-5 gnd Néron-Modell (DE-588)4233203-5 gnd Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Néron, Modèles de Variétés abéliennes Varietät Mathematik Néron-Modell Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001715001&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT boschsiegfried neronmodels AT lutkebohmertwerner neronmodels AT raynaudmichel neronmodels |