Non-representable six-functor formalisms

2024/09/30 by Chowdhury, Chirantan, D'Angelo, Alessandro · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.2409.20382

Abstract

In this article, we study the properties of motivic homotopy category SH_ext(X) developed by Chowdhury and Khan-Ravi for X a Nis-loc Stack. In particular, we compare the above construction with Voevodsky's original construction using NisLoc topology. Using the techniques developed by Liu-Zheng and Mann's notion of ∞-category of correspondences and abstract six-functor formalisms, we also extend the exceptional functors and extend properties like projection formula, base change and purity to the non-representable situation.

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• The Morel-Voevodsky Construction over Algebraic Stacks

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