Foundations of Grothendieck Duality for Diagrams of Schemes

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 f...

Full description

Bibliographic Details
Main Authors: Lipman, Joseph, Hashimoto, Mitsuyasu (Author)
Format: eBook
Language:English
Published: Berlin, Heidelberg Springer Berlin Heidelberg 2009, 2009
Edition:1st ed. 2009
Series:Lecture Notes in Mathematics
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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
  • 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