Algebraic geometry over C∞ -rings:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, Rhode Island
American Mathematical Society
[2019]
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| Series: | Memoirs of the American Mathematical Society
volume 260, number 1256 (fifth of 5 numbers) |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | v, 139 Seiten |
| ISBN: | 9781470436452 |
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MARC
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Record in the Search Index
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| adam_text | Contents Chapter 1. Introduction 1 Chapter 2. C00-rings 2.1. Two definitions of C^-ring 2.2. C^-rings as commutative Ił-algebras, and ideals 2.3. Local C^-rings, and localization 2.4. Fair C°°-rings 2.5. Pushouts of C^-rings 2.6. Flat ideals 5 5 7 8 10 13 15 Chapter 3. 17 The C°°-ring Cco{X) of a manifold X Chapter 4. C^-ringed spaces and C^-schemes 4.1. Some basic topology 4.2. Sheaves on topological spaces 4.3. C°°-ringed spaces and local C^-ringed spaces 4.4. The spectrum functor 4.5. Affine C°°-schemes and C^-schemes 4.6. Complete C^-rings 4.7. Partitions of unity 4.8. A criterion for affine C°°-schemes 4.9. Quotients of C^-schemes by finite groups 21 21 22 24 26 31 33 36 38 41 Chapter 5. Modules over C°°-rings and C^-schemes 5.1. Modules over C°°-rings 5.2. Cotangent modules of C^-rings 5.3. Sheaves of Οχ-modules on a C°°-ringed space (Χ,Οχ) 5.4. Sheaves on affine C^-schemes, MSpec and Г 5.5. Complete modules over C00-rings 5.6. Cotangent sheaves of C 30-schemes 45 45 46 50 51 56 58 Chapter 6. C°°-stacks 6.1. C^-stacks 6.2. Properties of 1-morphisms of C°°-stacks 6.3. Open C°°-substacks and open covers 6.4. The underlying topological space of a C°°-stack 6.5. Gluing C^-stacks by equivalences 61 61 63 65 66 68 Chapter 7. Deligne-Mumford C°°-stacks 7.1. Quotient C^-stacks, 1-morphisms, and 2-morphisms 7.2. Deligne-Mumford C°°-stacks 71 71 73 Ш
CONTENTS 7.3. 7.4. 7.5. 7.6. Characterizing Deligne-Mumford C°°-stacks Quotient C°°-stacks, 1- and 2-morphisms as local models for objects, 1- and 2-morphisms in DMC°°Sta Effective Deligne-Mumford C°°-stacks Orbifolds as Deligne-Mumford (C^-stacks Chapter 8. Sheaves on Deligne-Mumford C°°-stacks 8.1. Quasicoherent sheaves 8.2. Writing sheaves in terms of a groupoid presentation 8.3. Pullback of sheaves as a weak 2-functor 8.4. Cotangent sheaves of Deligne-Mumford C^-stacks 76 79 84 86 89 89 91 93 95 Chapter 9. Orbifold strata of C^-stacks 9.1. The definition of orbifold strata ffr,..., 9.2. Lifting 1-and 2-morphisms to orbifold strata 9.3. Orbifold strata of quotient C°°-stacks [X/G 9.4. Sheaves on orbifold strata 9.5. Sheaves on orbifold strata of quotients X/G 9.6. Cotangent sheaves of orbifold strata 99 100 107 108 109 113 114 Appendix A. Background material on stacks A.l. Introduction to 2-categories A.2. Grothendieck topologies, sites, prestacks, and stacks A.3. Descent theory on a site A.4. Properties of 1-morphisms A.5. Geometric stacks, and stacksassociated to groupoids 117 117 121 123 124 126 Bibliography 131 Glossary of Notation 135 Index 137
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| id | DE-604.BV046180266 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:37:28Z |
| institution | BVB |
| isbn | 9781470436452 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-031559814 |
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| physical | v, 139 Seiten |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Memoirs of the American Mathematical Society |
| series2 | Memoirs of the American Mathematical Society |
| spelling | Joyce, Dominic D. 1968- (DE-588)1043994483 aut Algebraic geometry over C∞ -rings Dominic Joyce Algebraic geometry over C [-infinity]-rings Providence, Rhode Island American Mathematical Society [2019] © 2019 v, 139 Seiten txt rdacontent n rdamedia nc rdacarrier Memoirs of the American Mathematical Society volume 260, number 1256 (fifth of 5 numbers) Memoirs of the American Mathematical Society volume 260, number 1256 (fifth of 5 numbers) (DE-604)BV008000141 1256 Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031559814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Joyce, Dominic D. 1968- Algebraic geometry over C∞ -rings Memoirs of the American Mathematical Society |
| title | Algebraic geometry over C∞ -rings |
| title_alt | Algebraic geometry over C [-infinity]-rings |
| title_auth | Algebraic geometry over C∞ -rings |
| title_exact_search | Algebraic geometry over C∞ -rings |
| title_full | Algebraic geometry over C∞ -rings Dominic Joyce |
| title_fullStr | Algebraic geometry over C∞ -rings Dominic Joyce |
| title_full_unstemmed | Algebraic geometry over C∞ -rings Dominic Joyce |
| title_short | Algebraic geometry over C∞ -rings |
| title_sort | algebraic geometry over c∞ rings |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=031559814&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV008000141 |
| work_keys_str_mv | AT joycedominicd algebraicgeometryovercrings AT joycedominicd algebraicgeometryovercinfinityrings |