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001 978-3-540-85420-3
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020 _a9783540854203
_9978-3-540-85420-3
024 7 _a10.1007/978-3-540-85420-3
_2doi
050 4 _aQA564-609
072 7 _aPBMW
_2bicssc
072 7 _aMAT012010
_2bisacsh
072 7 _aPBMW
_2thema
082 0 4 _a516.35
_223
100 1 _aLipman, Joseph.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aFoundations of Grothendieck Duality for Diagrams of Schemes
_h[electronic resource] /
_cby Joseph Lipman, Mitsuyasu Hashimoto.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2009.
300 _aX, 478 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1960
505 0 _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.
520 _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.
650 0 _aGeometry, algebraic.
650 0 _aAlgebra.
650 1 4 _aAlgebraic Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M11019
650 2 4 _aCategory Theory, Homological Algebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11035
700 1 _aHashimoto, Mitsuyasu.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783540854432
776 0 8 _iPrinted edition:
_z9783540854197
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v1960
856 4 0 _uhttps://doi.org/10.1007/978-3-540-85420-3
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c11444
_d11444