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 $\infty$-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.

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