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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
Database:WorldCat
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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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From the reviews: "The appearance of a well-planned, detailed and up-to-date exposition of a topic in abstract algebraic geometry is good news, and the book by J. Lipman and M. Hashimoto definitely Read more...

 
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