2026/07/08 by Adeel A. Khan
Mathematics · #math.AG
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 étale motivic spectra satisfy h-descent on noetherian finite-dimensional schemes with residue fields of uniformly bounded étale cohomological dimension. We also show that rational motivic cohomology satisfies arc-descent in weights ≤ 1, and we construct the ``forgetting supports'' isomorphism f_! ≃ f_* for a proper DM-type morphism of Artin stacks, in rational motivic sheaves.