Reflectors and localization: application to sheaf theory
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Dekker
1979
|
| Edition: | 1. print. |
| Series: | Lecture notes in pure and applied mathematics
41 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | 166 S. |
| ISBN: | 0824768442 |
Staff View
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Record in the Search Index
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| adam_text | CONTENTS
INTRODUCTION 1
CHAPTER I. THE RING THEORETIC SCENERY 5
1.1. Localization of Rings and Modules 5
1.2. Special Kernel Functors 10
1.3. Construction of Certain (Pre) Sheaves of Rings
and Modules 14
1.4. Fully Left Bounded Left Noetherian Classical Rings 21
1.5. Zariski Central Rings 25
CHAPTER II. REFLECTIONS ON REFLECTORS AND LOCALIZATION
IN GROTHENDIECK CATEGORIES 37
11.1. Categorical Background 37
11.2. Localization in Grothendieck Categories 42
11.3. Giraud Subcategories of a Complete Grothendieck
Category 51
11.4. Kernel Functors in Giraud Subcategories 55
11.5. The Main Example: Sheaves and Presheaves 65
11.6. Idempotent Filters 73
CHAPTER III. APPLICATION TO SHEAF THEORY 81
III.l (Pre) Sheaves of Rings and Modules of
Quotients: Generalities 81
III. 2. Local Kernel Functors 83
III.3. Idempotent Filters 87
III. 4. Ring Objects of Quotients 89
III. 5. T Functors in R Ker 93
III.6. Pointwise Localization of Presheaves 99
III.7 Strictly Local Kernel Functors and Coherent Modules 119
Modules 119
CHAPTER IV. APPLICATIONS 133
IV.1. Kerneled Spaces 133
IV.2. Affine Schemes 137
IV.3. Schemes 149
APPENDIX ODDS AND ENDS 156
A.I. A Functor p: rr(R) » Ens 156
A.2. Weakly Flabby Sheaves 156
REFERENCES 161
SUBJECT INDEX 165
|
| adam_txt |
CONTENTS
INTRODUCTION 1
CHAPTER I. THE RING THEORETIC SCENERY 5
1.1. Localization of Rings and Modules 5
1.2. Special Kernel Functors 10
1.3. Construction of Certain (Pre) Sheaves of Rings
and Modules 14
1.4. Fully Left Bounded Left Noetherian Classical Rings 21
1.5. Zariski Central Rings 25
CHAPTER II. REFLECTIONS ON REFLECTORS AND LOCALIZATION
IN GROTHENDIECK CATEGORIES 37
11.1. Categorical Background 37
11.2. Localization in Grothendieck Categories 42
11.3. Giraud Subcategories of a Complete Grothendieck
Category 51
11.4. Kernel Functors in Giraud Subcategories 55
11.5. The Main Example: Sheaves and Presheaves 65
11.6. Idempotent Filters 73
CHAPTER III. APPLICATION TO SHEAF THEORY 81
III.l (Pre) Sheaves of Rings and Modules of
Quotients: Generalities 81
III. 2. Local Kernel Functors 83
III.3. Idempotent Filters 87
III. 4. Ring Objects of Quotients 89
III. 5. T Functors in R Ker 93
III.6. Pointwise Localization of Presheaves 99
III.7 Strictly Local Kernel Functors and Coherent Modules 119
Modules 119
CHAPTER IV. APPLICATIONS 133
IV.1. Kerneled Spaces 133
IV.2. Affine Schemes 137
IV.3. Schemes 149
APPENDIX ODDS AND ENDS 156
A.I. A Functor p: rr(R) » Ens 156
A.2. Weakly Flabby Sheaves 156
REFERENCES 161
SUBJECT INDEX 165 |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| index_date | 2024-07-02T16:16:13Z |
| indexdate | 2024-07-09T20:50:55Z |
| institution | BVB |
| isbn | 0824768442 |
| language | English |
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| physical | 166 S. |
| publishDate | 1979 |
| publishDateSearch | 1979 |
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| series | Lecture notes in pure and applied mathematics |
| series2 | Lecture notes in pure and applied mathematics |
| spelling | Van Oystaeyen, Freddy 1947- Verfasser (DE-588)128792884 aut Reflectors and localization application to sheaf theory 1. print. New York [u.a.] Dekker 1979 166 S. txt rdacontent n rdamedia nc rdacarrier Lecture notes in pure and applied mathematics 41 Lokalisationstheorie (DE-588)4203492-9 gnd rswk-swf Nichtkommutativer Ring (DE-588)4246997-1 gnd rswk-swf Garbentheorie (DE-588)4155956-3 gnd rswk-swf Ringtheorie (DE-588)4126571-3 gnd rswk-swf Funktor (DE-588)4130706-9 gnd rswk-swf Funktor (DE-588)4130706-9 s DE-604 Garbentheorie (DE-588)4155956-3 s Nichtkommutativer Ring (DE-588)4246997-1 s Lokalisationstheorie (DE-588)4203492-9 s 1\p DE-604 Ringtheorie (DE-588)4126571-3 s 2\p DE-604 Verschoren, Alain H. M. J. Verfasser aut Lecture notes in pure and applied mathematics 41 (DE-604)BV005871364 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015334720&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Van Oystaeyen, Freddy 1947- Verschoren, Alain H. M. J. Reflectors and localization application to sheaf theory Lecture notes in pure and applied mathematics Lokalisationstheorie (DE-588)4203492-9 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd Garbentheorie (DE-588)4155956-3 gnd Ringtheorie (DE-588)4126571-3 gnd Funktor (DE-588)4130706-9 gnd |
| subject_GND | (DE-588)4203492-9 (DE-588)4246997-1 (DE-588)4155956-3 (DE-588)4126571-3 (DE-588)4130706-9 |
| title | Reflectors and localization application to sheaf theory |
| title_auth | Reflectors and localization application to sheaf theory |
| title_exact_search | Reflectors and localization application to sheaf theory |
| title_exact_search_txtP | Reflectors and localization application to sheaf theory |
| title_full | Reflectors and localization application to sheaf theory |
| title_fullStr | Reflectors and localization application to sheaf theory |
| title_full_unstemmed | Reflectors and localization application to sheaf theory |
| title_short | Reflectors and localization |
| title_sort | reflectors and localization application to sheaf theory |
| title_sub | application to sheaf theory |
| topic | Lokalisationstheorie (DE-588)4203492-9 gnd Nichtkommutativer Ring (DE-588)4246997-1 gnd Garbentheorie (DE-588)4155956-3 gnd Ringtheorie (DE-588)4126571-3 gnd Funktor (DE-588)4130706-9 gnd |
| topic_facet | Lokalisationstheorie Nichtkommutativer Ring Garbentheorie Ringtheorie Funktor |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015334720&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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