The Resource Auslander-Buchweitz approximations of equivariant modules, Mitsuyasu Hashimoto, (electronic resource)

Auslander-Buchweitz approximations of equivariant modules, Mitsuyasu Hashimoto, (electronic resource)

Label
Auslander-Buchweitz approximations of equivariant modules
Title
Auslander-Buchweitz approximations of equivariant modules
Statement of responsibility
Mitsuyasu Hashimoto
Creator
Subject
Genre
Language
  • eng
  • eng
Summary
This book, first piblished in 2000, contains research on commutative ring theory and representation theory
Member of
Cataloging source
MiAaPQ
http://library.link/vocab/creatorDate
1962-
http://library.link/vocab/creatorName
Hashimoto, Mitsuyasu
Dewey number
  • 512.55
  • 512/.55
Illustrations
illustrations
Index
index present
Language note
English
LC call number
QA169
LC item number
.H385 2000
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
London Mathematical Society lecture note series
Series volume
282
http://library.link/vocab/subjectName
  • Algebra, Homological
  • Modules (Algebra)
  • Commutative rings
Label
Auslander-Buchweitz approximations of equivariant modules, Mitsuyasu Hashimoto, (electronic resource)
Instantiates
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [267]-281) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Title; Copyright; Dedication; Contents; Introduction; Conventions and terminology; I Background Materials; 1 From homological algebra; 1.1 Yoneda's lemma; 1.2 Adjoint functors and limits; 1.3 Exact categories; 1.4 Derived categories and derived functors; 1.5 Extensions and Ext groups; 1.6 The cobar resolution; 1.7 Grothendieck categories; 1.8 Grothendieck topology and sheaf theory; 1.9 Noetherian categories and locally noetherian categories; 1.10 Semisimple objects in a Grothendieck category . . . .; 1.11 Full subcategories of an abelian category
  • 1.12 X-approximations and the Auslander-Buchweitz theory2 From commutative ring theory; 2.1 Flat modules and pure maps; 2.2 Mittag-Leffler modules; 2.3 Faithfully fiat morphisms and descent theory; 2.4 The I-depth; 2.5 Cohen-Macaulay, Gorenstein, and regular rings . . .; 2.6 Local cohomology; 2.7 Ring-theoretic properties of morphisms; 2.8 Betti numbers, Bass numbers and complete intersections; 2.9 Resolutions of perfect modules; 2.10 Dualizing complexes and canonical modules; 2.11 The duality of proper morphisms and rational singularities; 2.12 Summary of open loci results
  • 2.13 Normal flatness3 Hopf algebras over an arbitrary base; 3.1 Coalgebras and bialgebras; 3.2 Hopf algebras; 3.3 Comodules; 3.4 Sweedler's notation .; 3.5 Bicomodules, Horn and O; 3.6 The restriction and the induction; 3.7 Locally noetherian property; 3.8 The dual algebra of a coalgebra; 3.9 The dual coalgebra of an algebra; 3.10 Rational modules; 3.11 FPCP coalgebras and IFP coalgebras; 3.12 O and Horn of modules and comodules over a Hopf algebra; 3.13 The dual Hopf algebra; 3.14 Module algebras and comodule algebras; 3.15 Coalgebras and comodules over a scheme; 4 From representation theory
  • 4.1 Group schemes as faisceaux4.2 Rational representations of an algebraic group . . . .; 4.3 Algebraic tori; 4.4 Maximal tori, Borel subgroups, and reductive groups; 4.5 Split reductive groups; 4.6 General linear groups; 4.7 Representations of reductive groups over an algebraically closed field; 4.8 Universal module functors; 4.9 Tilting modules; 4.10 Cotilting modules; 5 Basics on equivariant modules; 5.1 Cocommutative Hopf algebra actions; 5.2 TorA and ExtA as A#U-modules; 5.3 (G,4)-modules; II Equivariant Modules; 1 Homological aspects of (G, ^4)-modules; 1.1 Construction of ExtA
  • 1.2 Equivariant modules of a split torus1.3 FPCP groups and IFP groups; 2 Matijevic-Roberts type theorem; 2.1 Stability of various loci; 2.2 Universal density of hyperalgebras; 2.3 A generalization to equivariant sheaves; 2.4 Matijevic-Roberts type theorem; III Highest Weight Theory; 1 Highest weight theory over a field; 1.1 Weak split highest weight coalgebras; 1.2 Weak highest weight theory; 1.3 Highest weight coalgebras and good comodules . . . .; 1.4 Weak highest weight coalgebras and good filtrations .; 2 Donkin systems; 2.1 U-acyclicity of flat complexes
  • 2.2 The definition and the existence of a Donkin system
Dimensions
unknown
Extent
1 online resource (299 p.)
Form of item
online
Isbn
9780511565762
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2610000000002844
  • (EBL)1182584
  • (SSID)ssj0000529631
  • (PQKBManifestationID)11350120
  • (PQKBTitleCode)TC0000529631
  • (PQKBWorkID)10560795
  • (PQKB)11737200
  • (UkCbUP)CR9780511565762
  • (MiAaPQ)EBC1182584
  • (EXLCZ)992610000000002844
Label
Auslander-Buchweitz approximations of equivariant modules, Mitsuyasu Hashimoto, (electronic resource)
Publication
Note
Description based upon print version of record
Bibliography note
Includes bibliographical references (p. [267]-281) and index
Carrier category
online resource
Carrier category code
cr
Content category
text
Content type code
txt
Contents
  • Cover; Title; Copyright; Dedication; Contents; Introduction; Conventions and terminology; I Background Materials; 1 From homological algebra; 1.1 Yoneda's lemma; 1.2 Adjoint functors and limits; 1.3 Exact categories; 1.4 Derived categories and derived functors; 1.5 Extensions and Ext groups; 1.6 The cobar resolution; 1.7 Grothendieck categories; 1.8 Grothendieck topology and sheaf theory; 1.9 Noetherian categories and locally noetherian categories; 1.10 Semisimple objects in a Grothendieck category . . . .; 1.11 Full subcategories of an abelian category
  • 1.12 X-approximations and the Auslander-Buchweitz theory2 From commutative ring theory; 2.1 Flat modules and pure maps; 2.2 Mittag-Leffler modules; 2.3 Faithfully fiat morphisms and descent theory; 2.4 The I-depth; 2.5 Cohen-Macaulay, Gorenstein, and regular rings . . .; 2.6 Local cohomology; 2.7 Ring-theoretic properties of morphisms; 2.8 Betti numbers, Bass numbers and complete intersections; 2.9 Resolutions of perfect modules; 2.10 Dualizing complexes and canonical modules; 2.11 The duality of proper morphisms and rational singularities; 2.12 Summary of open loci results
  • 2.13 Normal flatness3 Hopf algebras over an arbitrary base; 3.1 Coalgebras and bialgebras; 3.2 Hopf algebras; 3.3 Comodules; 3.4 Sweedler's notation .; 3.5 Bicomodules, Horn and O; 3.6 The restriction and the induction; 3.7 Locally noetherian property; 3.8 The dual algebra of a coalgebra; 3.9 The dual coalgebra of an algebra; 3.10 Rational modules; 3.11 FPCP coalgebras and IFP coalgebras; 3.12 O and Horn of modules and comodules over a Hopf algebra; 3.13 The dual Hopf algebra; 3.14 Module algebras and comodule algebras; 3.15 Coalgebras and comodules over a scheme; 4 From representation theory
  • 4.1 Group schemes as faisceaux4.2 Rational representations of an algebraic group . . . .; 4.3 Algebraic tori; 4.4 Maximal tori, Borel subgroups, and reductive groups; 4.5 Split reductive groups; 4.6 General linear groups; 4.7 Representations of reductive groups over an algebraically closed field; 4.8 Universal module functors; 4.9 Tilting modules; 4.10 Cotilting modules; 5 Basics on equivariant modules; 5.1 Cocommutative Hopf algebra actions; 5.2 TorA and ExtA as A#U-modules; 5.3 (G,4)-modules; II Equivariant Modules; 1 Homological aspects of (G, ^4)-modules; 1.1 Construction of ExtA
  • 1.2 Equivariant modules of a split torus1.3 FPCP groups and IFP groups; 2 Matijevic-Roberts type theorem; 2.1 Stability of various loci; 2.2 Universal density of hyperalgebras; 2.3 A generalization to equivariant sheaves; 2.4 Matijevic-Roberts type theorem; III Highest Weight Theory; 1 Highest weight theory over a field; 1.1 Weak split highest weight coalgebras; 1.2 Weak highest weight theory; 1.3 Highest weight coalgebras and good comodules . . . .; 1.4 Weak highest weight coalgebras and good filtrations .; 2 Donkin systems; 2.1 U-acyclicity of flat complexes
  • 2.2 The definition and the existence of a Donkin system
Dimensions
unknown
Extent
1 online resource (299 p.)
Form of item
online
Isbn
9780511565762
Media category
computer
Media type code
c
Specific material designation
remote
System control number
  • (CKB)2610000000002844
  • (EBL)1182584
  • (SSID)ssj0000529631
  • (PQKBManifestationID)11350120
  • (PQKBTitleCode)TC0000529631
  • (PQKBWorkID)10560795
  • (PQKB)11737200
  • (UkCbUP)CR9780511565762
  • (MiAaPQ)EBC1182584
  • (EXLCZ)992610000000002844

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