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Motivic homotopy theory of algebraic stacks

Chirantan Chowdhury

Vol. 9 (2024), No. 1, 1–22
Abstract

The aim of this paper is to extend the definition of motivic homotopy theory from schemes to a large class of algebraic stacks and establish a six functor formalism. The class of algebraic stacks that we consider includes many interesting examples: quasiseparated algebraic spaces, local quotient stacks and moduli stacks of vector bundles. We use the language of -categories developed by Lurie. Using the techniques developed by Ayoub, Gallauer and Vezzani, we extend the six functor formalism from schemes to our class of algebraic stacks. We also prove that the six functors satisfy properties like homotopy invariance, localization and purity.

Keywords
motivic homotopy theory, algebraic stacks
Mathematical Subject Classification
Primary: 14F42
Milestones
Received: 8 April 2022
Revised: 20 December 2023
Accepted: 11 January 2024
Published: 25 May 2024
Authors
Chirantan Chowdhury
University of Duisburg-Essen
Essen
Germany