Six-Functor-Formalisms on Higher Stacks

TL;DR

This paper demonstrates that six-functor formalisms on classical sites can be extended to higher geometric stacks, enabling broader applications in algebraic geometry and related fields.

Contribution

It establishes a canonical extension of derivator six-functor-formalisms to higher stacks, generalizing existing formalisms to more complex geometric objects.

Findings

Six-functor formalisms extend to higher geometric stacks.

Extensions apply to higher Nisnevich-Artin stacks.

Applications include broader classes of algebraic stacks.

Abstract

In this article, it is shown that derivator six-functor-formalisms on any (classical) site canonically extend to higher geometric stacks as defined by To\"en-Vezzosi under some natural locality conditions. As an application, it is shown that the six-functor-formalisms of Morel-Voevodsky-Ayoub extend to higher (Nisnevich-)Artin stacks locally of finite type over some fixed base scheme.