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arXiv · 2607.07137

Descendability and descent in topological weaves

Adeel A. Khan
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Abstract

We prove a criterion for a finitely presented surjection of algebraic spaces to be descendable in a topological weave. We apply this to show that \'etale motivic spectra satisfy $h$-descent on noetherian finite-dimensional schemes with residue fields of uniformly bounded \'etale cohomological dimension. We also show that rational motivic cohomology satisfies arc-descent in weights $\le 1$, and we construct the ``forgetting supports'' isomorphism $f_! \simeq f_*$ for a proper DM-type morphism of Artin stacks, in rational motivic sheaves.

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Adeel A. Khan. 2026-07-08. Descendability and descent in topological weaves. https://arxiv.org/abs/2607.07137

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