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On the Motivic Homotopy Type of Algebraic Stacks

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arxiv 2304.10631 v4 pith:TOIZDGJM submitted 2023-04-20 math.AG

Neeraj Deshmukh , Jack Hall This is my paper · ORCID
classification math.AG
keywords smoothalgebraiccategoryhomotopymotivestacksconsequenceconstruct
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abstract

We construct smooth presentations of algebraic stacks that are local epimorphisms in the Morel-Voevodsky $\mathbb{A}^1$-homotopy category. As a consequence we show that the motive of a smooth stack (in Voevodsky's triangulated category of motives) has many of the same properties as the motive of a smooth scheme.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

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

    math.AG 2026-08 conditional novelty 6.0 of 10

    A presentable six-functor formalism satisfying cohomological purity extends to Ind- and Pro-categories, defining motivic stable homotopy theory for ind-pro algebraic stacks such as the Hecke stack.

  2. Approximation theorems for classifying stacks over number fields

    math.NT 2025-07 conditional novelty 6.0 of 10

    For any connected linear algebraic group G over a number field, strong approximation with the Brauer-Manin obstruction holds for the classifying stack BG off any nonempty finite set of places.

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