An improvement on the base-change theorem and the functor $f^{!}$

Abstract

The major improvement in this paper is that we can extend the functor $(-{)}^{!}$ of Grothendieck duality to the unbounded derived category of sufficiently nice algebraic stacks. The original motivation came from formulas discovered by Avramov and Iyengar, linking Grothendieck duality with Hochscild homology and cohomology.

159 pages. This is the final, published version

References in corpus (4)

• Grothendieck-Neeman duality and the Wirthmüller isomorphism
• Perfect complexes on algebraic stacks
• Algebraic groups and compact generation of their derived categories of representations
• Proper local complete intersection morphisms preserve perfect complexes

Cited by in corpus (8)

• Conservative descent for semi-orthogonal decompositions
• The twisted inverse image pseudofunctor over commutative DG rings and perfect base change
• On the fundamental class of an essentially smooth scheme-map
• The relation between Grothendieck duality and Hochschild homology
• Grothendieck Duality and Transitivity II: Traces and Residues via Verdier's isomorphism
• The Moduli of Sections Has a Canonical Obstruction Theory
• Grothendieck Duality and Transitivity I: Formal Schemes
• Adjoints to a Fourier-Mukai transform