Zariskian filtrations:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1996
|
| Schriftenreihe: | K-monographs in mathematics
2 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | IX, 252 S. graph. Darst. |
| ISBN: | 0792341848 |
Internformat
MARC
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| 245 | 1 | 0 | |a Zariskian filtrations |c by Li Huishi and Freddy van Oystaeyen |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1996 | |
| 300 | |a IX, 252 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a K-monographs in mathematics |v 2 | |
| 650 | 7 | |a Modules filtrés |2 ram | |
| 650 | 4 | |a Filtered modules | |
| 650 | 4 | |a Filtered rings | |
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Datensatz im Suchindex
| _version_ | 1804125721546719232 |
|---|---|
| adam_text | CONTENTS
Introduction vn
Chapter I
Filtered Rings and Modules
§1. Topological Prerequisites 1
§2. Filtrations on Rings and Modules 3
§3. Complete Filtered Modules and Completions 10
3.1. Some properties of filtration topology 10
3.2. Equivalence of filtration topologies 11
3.3. Complete filtered modules 13
3.4. The completion of a filtered module 14
3.5. The existence of completions 23
§4. Filtrations and Associated Gradations 27
4.1. Preliminaries on gradations 27
4.2. Associated graded rings and modules 30
4.3. Dehomogenizations of grading to filtrations Rees rings (modules) 33
4.4. Finite intersection property and faithful filtrations 42
§5. Good Filtrations 46
§6. Projective and Injective Objects in i? filt 51
§7. Krull Dimension and Global Dimension of Filtered rings 60
7.1. Krull dimension of filtered rings 60
7.2. Global dimension of filtered rings 61
Chapter II
Zariskian Filtrations
§1. Flatness of Completion 70
1.1. Artin Rees property of filtrations 70
1.2. Flatness of completion 74
§2. Zariskian Filtrations 83
2.1. Definition and various characterizations 83
2.2. Examples of Zariskian filtration 87
§3. Lifting Structures of Zariski Rings 95
3.1. G(R) is gr Artinian, gr regular or Von Neuman gr regular 95
3.2. G(R) is a gr maximal order 96
§4. Zariskian Filtrations on Simple Artinian Rings 103
vi
§5. Global Dimension of Rees Rings Associated to Zariskian Filtrations 110
5.1. Addendum to graded homological algebra 110
5.2. Global dimension of Rees rings 118
§6. Kq of Rings with Zariskian Filtration 121
Chapter III
Auslander Regular Filtered (Graded) Rings
§1. Spectral Sequence Determined by a Filt complex 127
1.1. Spectral sequence determined by a filt complex 127
1.2. Spectral sequence determined by a complete filt complex 134
1.3. Double complexes and their spectral sequences 137
1.4. An application to Noetherian regular rings 144
§2. Auslander Regularity of Zariskian Filtered Rings 148
2.1. An introduction to Auslander regularity 148
2.2. Auslander regularity of Zariskian filtered rings 150
2.3. Auslander regularity of polynomial rings 153
2.4. Examples of Auslander regular rings 156
2.5. jR(M) = jC(R){G(M)) = Jz(M) = Jn(M) 157
§3. Auslander Regularity of Graded Rings 161
3.1. Auslander regularity of Rees rings 161
3.2. Good graded filtrations 164
3.3. gr Auslander regular rings are Auslander regular 168
3.4. Applications to invertible ideals 172
§4. Dimension Theory and Pure Module Theory over Zariskian Filtered
Rings with Auslander Regular Associated Graded Rings 176
4.1. Generalized Roos theorem and an application to Zariski rings 176
4.2. Pure (holonomic) modules over Zariski rings 183
4.3. Codimension calculation of Characteristic varieties 195
Chapter IV
Microlocalization of Filtered Rings and Modules,
Quantum Sections and Gauge Algebras
§1. Algebraic Microlocalization 200
§2. Quantum Sections and Microstructure Sheaves 211
§3. Generalized Gauge Algebras 227
§4. Quantum Sections of Enveloping Algebras 241
References 246
Subject Index 251
|
| any_adam_object | 1 |
| author | Li, Huishi 1955- Van Oystaeyen, Freddy 1947- |
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| dewey-full | 512/.4 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512/.4 |
| dewey-search | 512/.4 |
| dewey-sort | 3512 14 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV011222891 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:06:04Z |
| institution | BVB |
| isbn | 0792341848 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007529647 |
| oclc_num | 35096075 |
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| physical | IX, 252 S. graph. Darst. |
| publishDate | 1996 |
| publishDateSearch | 1996 |
| publishDateSort | 1996 |
| publisher | Kluwer |
| record_format | marc |
| series | K-monographs in mathematics |
| series2 | K-monographs in mathematics |
| spelling | Li, Huishi 1955- Verfasser (DE-588)123969034 aut Zariskian filtrations by Li Huishi and Freddy van Oystaeyen Dordrecht [u.a.] Kluwer 1996 IX, 252 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier K-monographs in mathematics 2 Modules filtrés ram Filtered modules Filtered rings Filtrierter Modul (DE-588)4154395-6 gnd rswk-swf Filtrierter Ring (DE-588)4154396-8 gnd rswk-swf Filtrierter Modul (DE-588)4154395-6 s DE-604 Filtrierter Ring (DE-588)4154396-8 s Van Oystaeyen, Freddy 1947- Verfasser (DE-588)128792884 aut K-monographs in mathematics 2 (DE-604)BV011222840 2 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007529647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Li, Huishi 1955- Van Oystaeyen, Freddy 1947- Zariskian filtrations K-monographs in mathematics Modules filtrés ram Filtered modules Filtered rings Filtrierter Modul (DE-588)4154395-6 gnd Filtrierter Ring (DE-588)4154396-8 gnd |
| subject_GND | (DE-588)4154395-6 (DE-588)4154396-8 |
| title | Zariskian filtrations |
| title_auth | Zariskian filtrations |
| title_exact_search | Zariskian filtrations |
| title_full | Zariskian filtrations by Li Huishi and Freddy van Oystaeyen |
| title_fullStr | Zariskian filtrations by Li Huishi and Freddy van Oystaeyen |
| title_full_unstemmed | Zariskian filtrations by Li Huishi and Freddy van Oystaeyen |
| title_short | Zariskian filtrations |
| title_sort | zariskian filtrations |
| topic | Modules filtrés ram Filtered modules Filtered rings Filtrierter Modul (DE-588)4154395-6 gnd Filtrierter Ring (DE-588)4154396-8 gnd |
| topic_facet | Modules filtrés Filtered modules Filtered rings Filtrierter Modul Filtrierter Ring |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007529647&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV011222840 |
| work_keys_str_mv | AT lihuishi zariskianfiltrations AT vanoystaeyenfreddy zariskianfiltrations |