Categories of commutative algebras:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Oxford
Clarendon Press
1992
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 271 S. |
| ISBN: | 0198535864 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804120088800919552 |
|---|---|
| adam_text | CONTENTS
INTRODUCTION 1
1 ZARISKI CATEGORIES 9
1.1 Codisjunctors 9
1.2 Definition of Zariski categories 15
1.3 Examples of Zariski categories 16
1.4 Products of objects and morphisms 25
1.5 Congruences 28
1.6 Flat morphisms 34
1.7 Flat epimorphisms and flat bimorphisms 37
1.8 Singular epimorphisms 39
1.9 The presingular factorization 42
2 CLASSICAL OBJECTS 45
2.1 Simple objects 45
2.2 Integral objects 49
2.3 Reduced objects 51
2.4 Radical congruences 54
2.5 Conjoint morphisms 60
2.6 Pseudo simple objects 63
2.7 Quasi primary objects 65
2.8 Primary objects 67
2.9 Singularly closed objects 68
2.10 Irreducible objects 70
2.11 Regular objects 72
2.12 Local objects 75
2.13 Localizations 78
3 SPECTRA 81
3.1 Prime spectra 81
3.2 Maximal and patch spectra 86
3.3 Topological interpretations 88
3.4 Structure sheaf on the prime spectrum 92
3.5 The cogenerating class of local objects 95
3.6 Local properties 98
viii CONTENTS
3.7 Semisingular epimorphisms 100
3.8 Subsets closed under generizations and affine subsets 103
3.9 Direct factor congruences and clopen subsets 105
3.10 Indecomposable objects 110
4 SCHEMES 112
4.1 Modelled spaces and locally modelled spaces 112
4.2 Prime spectrum of a modelled space 116
4.3 Schemes 121
4.4 Subschemes, immersions, and embeddings of schemes 125
4.5 Limits, colimits, and disjunctors of schemes 131
4.6 Locally finitely presentable schemes 134
5 JACOBSON ULTRASCHEMES 138
5.1 Jacobson objects 138
5.2 Jacobson schemes 141
5.3 Jacobson ultraschemes 142
6 ALGEBRAIC VARIETIES 147
6.1 Algebraically closed simple objects 148
6.2 Rational spectra 154
6.3 Rational Zariski categories 156
6.4 Reduced rational Zariski categories 160
6.5 Algebraic spaces and algebraic varieties 165
7 ZARISKI TOPOSES 169
7.1 The Zariski topos of a Zariski category 169
7.2 Modelled toposes on a Zariski category 172
7.3 Morphisms of Zariski categories 176
8 NEAT OBJECTS AND MORPHISMS 186
8.1 Preneat objects 187
8.2 Neat objects 191
8.3 Neatish objects 193
8.4 Purely unneat objects 197
8.5 Neatness of morphisms 197
8.6 The neatish factorization 200
8.7 Neatly closed objects 202
9 FLATNESS PROPERTIES 208
9.1 Flat, absolutely flat, and simply flat objects 208
CONTENTS ix
9.2 Flat, absolutely flat, and simply flat Zariski categories 211
9.3 Faithfully (reflexively, properly) flat morphisms 214
10 ETALE OBJECTS AND MORPHISMS 218
10.1 Etale objects 219
10.2 Etalish objects 220
10.3 Purely unetale objects 222
10.4 Etaleness of morphisms 223
10.5 Henselian objects 224
10.6 Strictly local objects 226
11 TERMINATORS 231
11.1 The term of a morphism 233
11.2 Preterminal morphisms 235
11.3 Interminable morphisms 236
11.4 Amalgamation properties 239
11.5 Terminators 240
11.6 Topological interpretations 245
11.7 Categories with finitely presentable terminators 248
11.8 Chevalley s theorem in Zariski categories 254
12 SOME CONSTRUCTIONS OF ZARISKI
CATEGORIES 256
12.1 Coslice Zariski categories 256
12.2 Functor Zariski categories 258
12.3 Zariski full subcategories 261
References 265
Index of symbols 267
Index of terms 269
|
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| id | DE-604.BV005899308 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:36:32Z |
| institution | BVB |
| isbn | 0198535864 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003693502 |
| oclc_num | 24630697 |
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| owner | DE-12 DE-739 DE-384 DE-634 |
| owner_facet | DE-12 DE-739 DE-384 DE-634 |
| physical | IX, 271 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Clarendon Press |
| record_format | marc |
| spelling | Diers, Yves Verfasser aut Categories of commutative algebras Yves Diers Oxford Clarendon Press 1992 IX, 271 S. txt rdacontent n rdamedia nc rdacarrier Algèbre abstraite ram Algèbres commutatives ram Catégories (Mathématiques) ram Categories (Mathematics) Commutative algebra Kategorie Mathematik (DE-588)4129930-9 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 gnd rswk-swf Kommutative Algebra (DE-588)4164821-3 s Kategorie Mathematik (DE-588)4129930-9 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003693502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Diers, Yves Categories of commutative algebras Algèbre abstraite ram Algèbres commutatives ram Catégories (Mathématiques) ram Categories (Mathematics) Commutative algebra Kategorie Mathematik (DE-588)4129930-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| subject_GND | (DE-588)4129930-9 (DE-588)4164821-3 |
| title | Categories of commutative algebras |
| title_auth | Categories of commutative algebras |
| title_exact_search | Categories of commutative algebras |
| title_full | Categories of commutative algebras Yves Diers |
| title_fullStr | Categories of commutative algebras Yves Diers |
| title_full_unstemmed | Categories of commutative algebras Yves Diers |
| title_short | Categories of commutative algebras |
| title_sort | categories of commutative algebras |
| topic | Algèbre abstraite ram Algèbres commutatives ram Catégories (Mathématiques) ram Categories (Mathematics) Commutative algebra Kategorie Mathematik (DE-588)4129930-9 gnd Kommutative Algebra (DE-588)4164821-3 gnd |
| topic_facet | Algèbre abstraite Algèbres commutatives Catégories (Mathématiques) Categories (Mathematics) Commutative algebra Kategorie Mathematik Kommutative Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003693502&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT diersyves categoriesofcommutativealgebras |