Six-Functor Formalisms

Abstract

These are lecture notes for a course in Winter 2022/23, updated and completed in October 2025. The goal of the lectures is to present some recent developments around six-functor formalisms, in particular: the abstract theory of 6-functor formalisms; the 2-category of cohomological correspondences, and resulting simplifications in the proofs of Poincar\'e--Verdier duality results; the relation between 6-functor formalisms and ``geometric rings''; many examples of 6-functor formalisms, both old and new.

Categories