Six-Functor Formalisms
Algebraic Geometry
2026-01-23 v2 Algebraic Topology
Category Theory
Number Theory
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.
Cite
@article{arxiv.2510.26269,
title = {Six-Functor Formalisms},
author = {Peter Scholze},
journal= {arXiv preprint arXiv:2510.26269},
year = {2026}
}
Comments
111 pages, v2: included functoriality of !-topology and extension to stacks