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.