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Author:   Joseph Lipman ,  Mitsuyasu Hashimoto
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2009 ed.
Volume:   1960
Dimensions:   Width: 15.50cm , Height: 2.50cm , Length: 23.50cm
Weight:   0.753kg
ISBN:  

9783540854197

ISBN 10:   3540854193
Pages:   478
Publication Date:   05 February 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of 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.- Boekstedt-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.

Reviews

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 has all the above qualities. ... get the book in its current state now than to wait for years until the authors produce a more unified presentation. To conclude, the book by Joseph Lipman and Mitsuyasu Hashimoto is an important contribution to an important task of explaining the main ideas of abstract algebraic geometry ... . (George Shabat, Bulletin of the London Mathematical Society, March, 2010)

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 has all the above qualities. ! get the book in its current state now than to wait for years until the authors produce a more unified presentation. To conclude, the book by Joseph Lipman and Mitsuyasu Hashimoto is an important contribution to an important task of explaining the main ideas of abstract algebraic geometry ! . (George Shabat, Bulletin of the London Mathematical Society, March, 2010)

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