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arXiv · 2608.09726

Abstract Six-Functor Formalisms: Extension to Ind- and Pro- Categories and Functorial Cohomological Purity

Chirantan Chowdhury
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Abstract

In this article, we study two consequences of abstract six-functor formalisms. Firstly, we show that an abstract six-functor formalism can be extended to specific Ind- and Pro- categories of geometric setups. As an application, we can define the motivic stable homotopy theory for ind-pro-algebraic stacks such as the Hecke stack. Secondly, we also show that Cohomological Purity is functorial using the multisimplicial language developed by Liu-Zheng.

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BibTeXRIS

Chirantan Chowdhury. 2026-08-10. Abstract Six-Functor Formalisms: Extension to Ind- and Pro- Categories and Functorial Cohomological Purity. https://arxiv.org/abs/2608.09726

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