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Foundations of Grothendieck duality for diagrams of schemes

Author: Joseph Lipman; Mitsuyasu Hashimoto
Publisher: Berlin : Springer, cop. 2009.
Series: Lecture notes in mathematics, 1960
Edition/Format:   Print book : EnglishView all editions and formats

Part One of this book covers the abstract foundations of Grothendieck duality theory for schemes in part with noetherian hypotheses and with some refinements for maps of finite tor-dimension. Part  Read more...


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Document Type: Book
All Authors / Contributors: Joseph Lipman; Mitsuyasu Hashimoto
ISBN: 9783540854197 3540854193
OCLC Number: 470933726
Notes: Notes bibliogr.
Description: 1 vol. (X-478 p.) : ill. ; 24 cm.
Contents: Joseph 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.- Bokstedt-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.
Series Title: Lecture notes in mathematics, 1960
Responsibility: Joseph Lipman, Mitsuyasu Hashimoto.
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