Galois theories:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2001
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | Cambridge studies in advanced mathematics
72 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIV, 341 S. graph. Darst. |
| ISBN: | 0521803098 |
Internformat
MARC
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| 100 | 1 | |a Borceux, Francis |d 1948- |e Verfasser |0 (DE-588)11084825X |4 aut | |
| 245 | 1 | 0 | |a Galois theories |c Francis Borceux ; George Janelidze |
| 250 | |a 1. publ. | ||
| 264 | 1 | |a Cambridge |b Cambridge Univ. Press |c 2001 | |
| 300 | |a XIV, 341 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Cambridge studies in advanced mathematics |v 72 | |
| 650 | 4 | |a Galois, Théorie de | |
| 650 | 7 | |a Galois-theorie |2 gtt | |
| 650 | 7 | |a Teoria de galois |2 larpcal | |
| 650 | 7 | |a Álgebra |2 larpcal | |
| 650 | 4 | |a Galois theory | |
| 650 | 0 | 7 | |a Galois-Theorie |0 (DE-588)4155901-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Galois-Theorie |0 (DE-588)4155901-0 |D s |
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| 700 | 1 | |a Janelidze, George |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804128787364839424 |
|---|---|
| adam_text | Contents
Preface page vii
1 Classical Galois theory 1
1.1 Algebraic extensions 1
1.2 Separable extensions 4
1.3 Normal extensions 6
1.4 Galois extensions 8
2 Galois theory of Grothendieck 15
2.1 Algebras on a field 15
2.2 Extension of scalars 20
2.3 Split algebras 23
2.4 The Galois equivalence 27
3 Infinitary Galois theory 36
3.1 Finitary Galois subextensions 36
3.2 Infinitary Galois groups 39
3.3 Classical infinitary Galois theory 44
3.4 Profinite topological spaces 47
3.5 Infinitary extension of the Galois theory of Grothendieck 56
4 Categorical Galois theory of commutative rings 65
4.1 Stone duality 65
4.2 Pierce representation of a commutative ring 72
4.3 The adjoint of the spectrum functor 80
4.4 Descent morphisms 91
4.5 Morphisms of Galois descent 98
4.6 Internal presheaves 102
4.7 The Galois theorem for rings 106
v
vi Contents
5 Categorical Galois theorem and factorization systems 116
5.1 The abstract categorical Galois theorem 117
5.2 Central extensions of groups 127
5.3 Factorization systems 144
5.4 Reflective factorization systems 149
5.5 Semi exact reflections 156
5.6 Connected components of a space 168
5.7 Connected components of a compact Hausdorff space 170
5.8 The monotone light factorization 177
6 Covering maps 186
6.1 Categories of abstract families 186
6.2 Some limits in Fam(A) 189
6.3 Involving extensivity 193
6.4 Local connectedness and etale maps 197
6.5 Localization and covering morphisms 201
6.6 Classification of coverings 207
6.7 The Chevalley fundamental group 212
6.8 Path and simply connected spaces 216
7 Non galoisian Galois theory 225
7.1 Internal presheaves on an internal groupoid 225
7.2 Internal precategories and their presheaves 241
7.3 A factorization system for functors 246
7.4 Generalized descent theory 251
7.5 Generalized Galois theory 258
7.6 Classical Galois theories 261
7.7 Grothendieck toposes 266
7.8 Geometric morphisms 274
7.9 Two dimensional category theory 287
7.10 The Joyal Tierney theorem 294
Appendix Final remarks 304
A.I Separable algebras 304
A.2 Back to the classical Galois theory 310
A.3 Exhibiting some links 316
A.4 A short summary of further results and developments 328
Bibliography 331
Index of symbols 336
General index 338
|
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| author | Borceux, Francis 1948- Janelidze, George |
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| dewey-full | 512/.3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.3 |
| dewey-search | 512/.3 |
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| discipline | Mathematik |
| edition | 1. publ. |
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| id | DE-604.BV013942785 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:54:47Z |
| institution | BVB |
| isbn | 0521803098 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-009539841 |
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| physical | XIV, 341 S. graph. Darst. |
| publishDate | 2001 |
| publishDateSearch | 2001 |
| publishDateSort | 2001 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | Cambridge studies in advanced mathematics |
| series2 | Cambridge studies in advanced mathematics |
| spelling | Borceux, Francis 1948- Verfasser (DE-588)11084825X aut Galois theories Francis Borceux ; George Janelidze 1. publ. Cambridge Cambridge Univ. Press 2001 XIV, 341 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge studies in advanced mathematics 72 Galois, Théorie de Galois-theorie gtt Teoria de galois larpcal Álgebra larpcal Galois theory Galois-Theorie (DE-588)4155901-0 gnd rswk-swf Galois-Theorie (DE-588)4155901-0 s DE-604 Janelidze, George Verfasser aut Cambridge studies in advanced mathematics 72 (DE-604)BV000003678 72 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009539841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Borceux, Francis 1948- Janelidze, George Galois theories Cambridge studies in advanced mathematics Galois, Théorie de Galois-theorie gtt Teoria de galois larpcal Álgebra larpcal Galois theory Galois-Theorie (DE-588)4155901-0 gnd |
| subject_GND | (DE-588)4155901-0 |
| title | Galois theories |
| title_auth | Galois theories |
| title_exact_search | Galois theories |
| title_full | Galois theories Francis Borceux ; George Janelidze |
| title_fullStr | Galois theories Francis Borceux ; George Janelidze |
| title_full_unstemmed | Galois theories Francis Borceux ; George Janelidze |
| title_short | Galois theories |
| title_sort | galois theories |
| topic | Galois, Théorie de Galois-theorie gtt Teoria de galois larpcal Álgebra larpcal Galois theory Galois-Theorie (DE-588)4155901-0 gnd |
| topic_facet | Galois, Théorie de Galois-theorie Teoria de galois Álgebra Galois theory Galois-Theorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009539841&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000003678 |
| work_keys_str_mv | AT borceuxfrancis galoistheories AT janelidzegeorge galoistheories |