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Lisse extensions of weaves

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arxiv 2501.04114 v2 pith:LHAXTQIV submitted 2025-01-07 math.AG math.AT

Adeel A. Khan This is my paper · ORCID
classification math.AGmath.AT
keywords lisseextensionstacksartinformalismschemesweavealgebraic
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Any sheaf theory on schemes extends canonically to Artin stacks via a procedure called lisse extension. In this paper we show that lisse extension preserves the formalism of Grothendieck's six operations: more precisely, the lisse extension of a weave on schemes determines a weave on (higher) Artin stacks. The setup is general enough to apply to the stable motivic homotopy category with the six functor formalism of Voevodsky-Ayoub-Cisinski-Deglise, for instance, and is not specific to algebraic geometry: for example, it also applies to sheaves of spectra on topological stacks.

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  1. Descendability and descent in topological weaves

    math.AG 2026-07 accept novelty 7.0 of 10

    Finitely presented surjections of algebraic spaces are descendable in topological weaves, yielding v-descent for rational motivic sheaves and h-descent for étale motivic spectra under bounded cohomological dimension.

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