LEADER 05427nam 22006135 450 001 996466538203316 005 20200705044740.0 010 $a3-540-85420-7 024 7 $a10.1007/978-3-540-85420-3 035 $a(CKB)1000000000714644 035 $a(SSID)ssj0000317762 035 $a(PQKBManifestationID)11292437 035 $a(PQKBTitleCode)TC0000317762 035 $a(PQKBWorkID)10308024 035 $a(PQKB)10443677 035 $a(DE-He213)978-3-540-85420-3 035 $a(MiAaPQ)EBC3064003 035 $a(PPN)13412605X 035 $a(EXLCZ)991000000000714644 100 $a20100301d2009 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt 182 $cc 183 $acr 200 10$aFoundations of Grothendieck Duality for Diagrams of Schemes$b[electronic resource] /$fby Joseph Lipman, Mitsuyasu Hashimoto 205 $a1st ed. 2009. 210 1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009. 215 $a1 online resource (X, 478 p.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1960 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-540-85419-3 320 $aIncludes bibliographical references and indexes. 327 $aJoseph Lipman: Notes on Derived Functors and Grothendieck Duality -- Derived and Triangulated Categories -- Derived Functors -- Derived Direct and Inverse Image -- Abstract Grothendieck Duality for Schemes -- Mitsuyasu Hashimoto: Equivariant Twisted Inverses -- Commutativity of Diagrams Constructed from a Monoidal Pair of Pseudofunctors -- Sheaves on Ringed Sites -- Derived Categories and Derived Functors of Sheaves on Ringed Sites -- Sheaves over a Diagram of S-Schemes -- The Left and Right Inductions and the Direct and Inverse Images -- Operations on Sheaves Via the Structure Data -- Quasi-Coherent Sheaves Over a Diagram of Schemes -- Derived Functors of Functors on Sheaves of Modules Over Diagrams of Schemes -- Simplicial Objects -- Descent Theory -- Local Noetherian Property -- Groupoid of Schemes -- Bökstedt?Neeman Resolutions and HyperExt Sheaves -- The Right Adjoint of the Derived Direct Image Functor -- Comparison of Local Ext Sheaves -- The Composition of Two Almost-Pseudofunctors -- The Right Adjoint of the Derived Direct Image Functor of a Morphism of Diagrams -- Commutativity of Twisted Inverse with Restrictions -- Open Immersion Base Change -- The Existence of Compactification and Composition Data for Diagrams of Schemes Over an Ordered Finite Category -- Flat Base Change -- Preservation of Quasi-Coherent Cohomology -- Compatibility with Derived Direct Images -- Compatibility with Derived Right Inductions -- Equivariant Grothendieck's Duality -- Morphisms of Finite Flat Dimension -- Cartesian Finite Morphisms -- Cartesian Regular Embeddings and Cartesian Smooth Morphisms -- Group Schemes Flat of Finite Type -- Compatibility with Derived G-Invariance -- Equivariant Dualizing Complexes and Canonical Modules -- A Generalization of Watanabe's Theorem -- Other Examples of Diagrams of Schemes. 330 $aThe first part written by Joseph Lipman, accessible to mid-level graduate students, is a full exposition of the abstract foundations of Grothendieck duality theory for schemes (twisted inverse image, tor-independent base change,...), in part without noetherian hypotheses, and with some refinements for maps of finite tor-dimension. The ground is prepared by a lengthy treatment of the rich formalism of relations among the derived functors, for unbounded complexes over ringed spaces, of the sheaf functors tensor, hom, direct and inverse image. Included are enhancements, for quasi-compact quasi-separated schemes, of classical results such as the projection and Künneth isomorphisms. In the second part, written independently by Mitsuyasu Hashimoto, the theory is extended to the context of diagrams of schemes. This includes, as a special case, an equivariant theory for schemes with group actions. In particular, after various basic operations on sheaves such as (derived) direct images and inverse images are set up, Grothendieck duality and flat base change for diagrams of schemes are proved. Also, dualizing complexes are studied in this context. As an application to group actions, we generalize Watanabe's theorem on the Gorenstein property of invariant subrings. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v1960 606 $aAlgebraic geometry 606 $aCategory theory (Mathematics) 606 $aHomological algebra 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aCategory Theory, Homological Algebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11035 615 0$aAlgebraic geometry. 615 0$aCategory theory (Mathematics). 615 0$aHomological algebra. 615 14$aAlgebraic Geometry. 615 24$aCategory Theory, Homological Algebra. 676 $a516.35 686 $a14A20$a18E30$a14F99$a18A99$a18F99$a14L30$2msc 700 $aLipman$b Joseph$4aut$4http://id.loc.gov/vocabulary/relators/aut$059702 702 $aHashimoto$b Mitsuyasu$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a996466538203316 996 $aFoundations of Grothendieck Duality for Diagrams of Schemes$92831947 997 $aUNISA LEADER 01095nam0 2200265 i 450 001 VAN0041342 005 20070703120000.0 010 $a88-243-1590-9 100 $a20060228d2005 |0itac50 ba 101 $aita 102 $aIT 105 $a|||| ||||| 200 1 $aˆI ‰modelli familiari tra diritti e servizi$eLecce 24-25 settembre 2004$fa cura di Marilena Gorgoni 210 $aNapoli$cJovene$dc2005 215 $aXI, 463 p.$d19 cm. 410 1$1001VAN0060190$12001 $aCollana della Facoltà di giurisprudenza, Università degli studi di Lecce. N. S$1210 $aNapoli$cJovene.$v11 620 $dNapoli$3VANL000005 702 1$aGorgoni$bMarilena$3VANV032642 712 $aJovene $3VANV107888$4650 801 $aIT$bSOL$c20230707$gRICA 899 $aBIBLIOTECA DEL DIPARTIMENTO DI GIURISPRUDENZA$1IT-CE0105$2VAN00 912 $aVAN0041342 950 $aBIBLIOTECA DEL DIPARTIMENTO DI GIURISPRUDENZA$d00CONS XV.Ef.139 $e00 31519 20060228 996 $aModelli familiari tra diritti e servizi$9740904 997 $aUNICAMPANIA