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arXiv · 2501.04114

Lisse extensions of weaves

Adeel A. Khan
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Abstract

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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Adeel A. Khan. 2025-01-07. Lisse extensions of weaves. https://arxiv.org/abs/2501.04114

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