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Derived category methods in commutative algebra

Record Type:	Electronic resources : Monograph/item
Title/Author:	Derived category methods in commutative algebra/ by Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm.
Author:	Christensen, Lars Winther.
other author:	Foxby, Hans-Bjørn.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	xxiii, 1119 p. :ill., digital ;24 cm.
[NT 15003449]:	1 Modules -- 2 Complexes -- 3 Categorical Constructions -- 4 Equivalences and Isomorphisms -- 5 Resolutions -- 6 The Derived Category -- 7 Derived Functors -- 8 Homological Dimensions -- 9 Gorenstein Homological Dimensions -- 10 Dualizing Complexes -- 11 Torsion and Completion -- 12 A Brief for Commutative Ring Theorists -- 13 Derived Torsion and Completion -- 14 Krull Dimension, Depth, and Width -- 15 Support Theories -- 16 Homological Invariants over Local Rings -- 17 Going Local -- 18 Dualities and Cohen-Macaulay Rings -- 19 Gorenstein Dimensions and Gorenstein Rings -- 20 Global Dimension and Regular Rings -- APPENDIX A: Acyclicity and Boundedness -- APPENDIX B: Minimality -- APPENDIX C: Structure of Injective Modules -- APPENDIX D: Projective Dimension of Flat Modules -- APPENDIX E: Triangulated Categories.
Contained By:	Springer Nature eBook
Subject:	Commutative algebra. -
Online resource:	https://doi.org/10.1007/978-3-031-77453-9
ISBN:	9783031774539

Derived category methods in commutative algebra
Christensen, Lars Winther.

Derived category methods in commutative algebra[electronic resource] /by Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm. - Cham :Springer Nature Switzerland :2024. - xxiii, 1119 p. :ill., digital ;24 cm. - Springer monographs in mathematics,2196-9922. - Springer monographs in mathematics..

1 Modules -- 2 Complexes -- 3 Categorical Constructions -- 4 Equivalences and Isomorphisms -- 5 Resolutions -- 6 The Derived Category -- 7 Derived Functors -- 8 Homological Dimensions -- 9 Gorenstein Homological Dimensions -- 10 Dualizing Complexes -- 11 Torsion and Completion -- 12 A Brief for Commutative Ring Theorists -- 13 Derived Torsion and Completion -- 14 Krull Dimension, Depth, and Width -- 15 Support Theories -- 16 Homological Invariants over Local Rings -- 17 Going Local -- 18 Dualities and Cohen-Macaulay Rings -- 19 Gorenstein Dimensions and Gorenstein Rings -- 20 Global Dimension and Regular Rings -- APPENDIX A: Acyclicity and Boundedness -- APPENDIX B: Minimality -- APPENDIX C: Structure of Injective Modules -- APPENDIX D: Projective Dimension of Flat Modules -- APPENDIX E: Triangulated Categories.

Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck's Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand. This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings. The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject.

ISBN: 9783031774539

Standard No.: 10.1007/978-3-031-77453-9doiSubjects--Topical Terms:

604140
Commutative algebra.

LC Class. No.: QA251.3

Dewey Class. No.: 512.44

Derived category methods in commutative algebra
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100 1 $a Christensen, Lars Winther. $3 1071457
245 1 0 $a Derived category methods in commutative algebra $h [electronic resource] / $c by Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm.
260 $a Cham : $b Springer Nature Switzerland : $b Imprint: Springer, $c 2024.
300 $a xxiii, 1119 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer monographs in mathematics, $x 2196-9922
505 0 $a 1 Modules -- 2 Complexes -- 3 Categorical Constructions -- 4 Equivalences and Isomorphisms -- 5 Resolutions -- 6 The Derived Category -- 7 Derived Functors -- 8 Homological Dimensions -- 9 Gorenstein Homological Dimensions -- 10 Dualizing Complexes -- 11 Torsion and Completion -- 12 A Brief for Commutative Ring Theorists -- 13 Derived Torsion and Completion -- 14 Krull Dimension, Depth, and Width -- 15 Support Theories -- 16 Homological Invariants over Local Rings -- 17 Going Local -- 18 Dualities and Cohen-Macaulay Rings -- 19 Gorenstein Dimensions and Gorenstein Rings -- 20 Global Dimension and Regular Rings -- APPENDIX A: Acyclicity and Boundedness -- APPENDIX B: Minimality -- APPENDIX C: Structure of Injective Modules -- APPENDIX D: Projective Dimension of Flat Modules -- APPENDIX E: Triangulated Categories.
520 $a Derived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck's Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand. This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings. The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject.
650 0 $a Commutative algebra. $3 604140
650 0 $a Categories (Mathematics) $3 525955
650 1 4 $a Category Theory, Homological Algebra. $3 899944
650 2 4 $a Commutative Rings and Algebras. $3 891076
700 1 $a Foxby, Hans-Bjørn. $3 3735049
700 1 $a Holm, Henrik. $3 3735050
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
830 0 $a Springer monographs in mathematics. $3 1535313
856 4 0 $u https://doi.org/10.1007/978-3-031-77453-9
950 $a Mathematics and Statistics (SpringerNature-11649)