Overview
- Includes supplementary material: sn.pub/extras
Part of the book series: Lecture Notes in Mathematics (LNM, volume 1960)
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Table of contents (39 chapters)
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Front Matter
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Joseph Lipman: Notes on Derived Functors and Grothendieck Duality
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Front Matter
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Back Matter
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Mitsuyasu Hashimoto: Equivariant Twisted Inverses
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Front Matter
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Keywords
About this book
The 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.
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Authors and Affiliations
Bibliographic Information
Book Title: Foundations of Grothendieck Duality for Diagrams of Schemes
Authors: Joseph Lipman, Mitsuyasu Hashimoto
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-540-85420-3
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2009
Softcover ISBN: 978-3-540-85419-7Published: 05 February 2009
eBook ISBN: 978-3-540-85420-3Published: 07 March 2009
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: X, 478
Topics: Algebraic Geometry, Category Theory, Homological Algebra