Algebraic geometry and commutative algebra: Siegfried Bosch
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London
Springer
[2013]
|
| Series: | Universitext
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 504 Seiten Diagramme |
| ISBN: | 9781447148289 |
Staff View
MARC
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| 100 | 1 | |a Bosch, Siegfried |d 1944- |e Verfasser |0 (DE-588)106950827 |4 aut | |
| 245 | 1 | 0 | |a Algebraic geometry and commutative algebra |b Siegfried Bosch |
| 264 | 1 | |a London |b Springer |c [2013] | |
| 264 | 4 | |c © 2013 | |
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Record in the Search Index
| _version_ | 1804149653474639872 |
|---|---|
| adam_text | Contents
Part A. Commutative Algebra
..................... 1
Introduction
................................ 1
1
Rings and Modules
............................ 7
1.1
Rings and Ideals
.......................... 9
1.2
Local Rings and Localization of Rings
.............. 18
1.3
Radicals
...............................
2G
1.4
Modules
............................... 31
1.5
Finiteness Conditions and the Snake Lemma
........... 38
2
The Theory of Noetherian Rings
.................... 55
2.1
Primary Decomposition of Ideals
................. 57
2.2
Artinian Rings and Modules
.................... 66
2.3
The Artin-Rees Lemma
...................... 71
2.4
Krull Dimension
........................... 74
3
Integral Extensions
........................... 83
3.1
Integral Dependence
........................ 85
3.2
Noether Normalization and Hubert s
Nullstellensatz....... 91
3.3
The Cohen-Seidenberg Theorems
................. 96
4
Extension of Coefficients and Descent
................. 103
4.1
Tensor Products
........................... 107
4.2
Flat Modules
............................ 113
4.3
Extension of Coefficients
...................... 123
4.4
Faithfully Flat Descent of Module Properties
........... 131
4.5
Categories and Functors
...................... 138
4.6
Faithfully Flat Descent of Modules and their Morphisms
.... 143
5
Homologieal Methods: Ext and Tor
................... 157
5.1
Complexes, Homology, and Cohomology
............. 159
5.2
The Tor Modules
.......................... 172
5.3
Injective Resolutions
........................ 181
5.4
The Ext. Modules
.......................... 187
X
Contents
Part B.
Algebraic Geometry
...................... 193
Introduction
................................ 193
6 Affine
Schemes and Basic Constructions
................ 201
6.1
The Spectrum of a Ring
...................... 203
6.2
Functorial Properties of Spectra
.................. 212
6.3
Presheaves and Sheaves
....................... 216
6.4
Inductive and
Projective
Limits
.................. 222
6.5
Morphisms of Sheaves and Sheafification
............. 232
6.6
Construction of
Affine
Schemes
.................. 241
6.7
The
Affine n-Space......................... 255
6.8
Quasi-Coherent Modules
...................... 257
6.9
Direct and Inverse Images of Module Sheaves
.......... 266
7
Techniques of Global Schemes
..................... 277
7.1
Construction of Schemes by Gluing
................ 282
7.2
Fiber Products
........................... 294
7.3
Subschemes and Immersions
.................... 304
7.4
Separated Schemes
......................... 312
7.5
Noetherian Schemes and their Dimension
............. 318
7.6
Čech Cohomology
.......................... 322
7.7
Grothendieck
Cohomology
..................... 330
8
Etale
and Smooth Morphisms
...................... 341
8.1
Differential Forms
.......................... 343
8.2
Sheaves of Differential Forms
.................... 356
8.3
Morphisms of Finite Type and of Finite Presentation
...... 360
8.4
Unramified Morphisms
....................... 365
8.5
Smooth Morphisms
......................... 374
9
Projective
Schemes and Proper Morphisms
.............. 399
9.1
Homogeneous Prime Spectra as Schemes
............. 403
9.2
Invertible Sheaves and
Serre
Twists
................ 418
9.3
Divisors
............................... 431
9.4
Global Sections of Invertible Sheaves
............... 446
9.5
Proper Morphisms
......................... 462
9.6
Abelian Varieties are
Projective
.................. 477
Literature
.................................. 485
Glossary of Notations
............................ 487
Index
..................................... 495
|
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| id | DE-604.BV040575776 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T00:26:27Z |
| institution | BVB |
| isbn | 9781447148289 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025403031 |
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| physical | X, 504 Seiten Diagramme |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series2 | Universitext |
| spelling | Bosch, Siegfried 1944- Verfasser (DE-588)106950827 aut Algebraic geometry and commutative algebra Siegfried Bosch London Springer [2013] © 2013 X, 504 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Universitext Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s Kommutative Algebra (DE-588)4164821-3 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4471-4829-6 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025403031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bosch, Siegfried 1944- Algebraic geometry and commutative algebra Siegfried Bosch Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4001161-6 (DE-588)4164821-3 |
| title | Algebraic geometry and commutative algebra Siegfried Bosch |
| title_auth | Algebraic geometry and commutative algebra Siegfried Bosch |
| title_exact_search | Algebraic geometry and commutative algebra Siegfried Bosch |
| title_full | Algebraic geometry and commutative algebra Siegfried Bosch |
| title_fullStr | Algebraic geometry and commutative algebra Siegfried Bosch |
| title_full_unstemmed | Algebraic geometry and commutative algebra Siegfried Bosch |
| title_short | Algebraic geometry and commutative algebra |
| title_sort | algebraic geometry and commutative algebra siegfried bosch |
| title_sub | Siegfried Bosch |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Algebraische Geometrie Kommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025403031&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT boschsiegfried algebraicgeometryandcommutativealgebrasiegfriedbosch |