LEADER 03878nam 22006615 450 001 9910917193003321 005 20250527192503.0 010 $a9783031774539 010 $a3031774531 024 7 $a10.1007/978-3-031-77453-9 035 $a(MiAaPQ)EBC31815230 035 $a(Au-PeEL)EBL31815230 035 $a(CKB)36822891200041 035 $a(OCoLC)1477221134 035 $a(DE-He213)978-3-031-77453-9 035 $a(EXLCZ)9936822891200041 100 $a20241205d2024 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDerived Category Methods in Commutative Algebra /$fby Lars Winther Christensen, Hans-Bjørn Foxby, Henrik Holm 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (1130 pages) 225 1 $aSpringer Monographs in Mathematics,$x2196-9922 311 08$a9783031774522 311 08$a3031774523 327 $a1 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. 330 $aDerived category methods entered commutative algebra in the latter half of the 1960s, providing, among other things, a framework for a clear formulation of Grothendieck?s Local Duality Theorem. Since then, their impact on the field has steadily grown and continues to expand. This book guides readers familiar with rings and modules through the construction of the associated derived category and its triangulated functors. In this context, it develops theories of categorical equivalences for subcategories and homological invariants of objects. The second half of the book focuses on applications to commutative Noetherian rings. The book can be used as a text for graduate courses, both introductory and advanced, and is intended to serve as a reference for researchers in commutative algebra and related fields. To accommodate readers new to homological algebra, it offers a significantly higher level of detail than most existing texts on the subject. 410 0$aSpringer Monographs in Mathematics,$x2196-9922 606 $aAlgebra, Homological 606 $aCommutative algebra 606 $aCommutative rings 606 $aCategory Theory, Homological Algebra 606 $aCommutative Rings and Algebras 606 $aÀlgebra commutativa$2thub 606 $aÀlgebra homològica$2thub 608 $aLlibres electrònics$2thub 615 0$aAlgebra, Homological. 615 0$aCommutative algebra. 615 0$aCommutative rings. 615 14$aCategory Theory, Homological Algebra. 615 24$aCommutative Rings and Algebras. 615 7$aÀlgebra commutativa 615 7$aÀlgebra homològica 676 $a512.6 700 $aChristensen$b Lars Winther$063027 701 $aFoxby$b Hans-Bjø$01779651 701 $aHolm$b Henrik$01779652 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910917193003321 996 $aDerived Category Methods in Commutative Algebra$94303222 997 $aUNINA