English

A pro-cdh topology on formal schemes

Algebraic Geometry 2024-09-24 v1

Abstract

We introduce a pro-cdh topology on formal schemes and prove that the \infty-topos of pro-cdh sheaves of spaces has an optimal bound of homotopy dimension. This remedies a defect for a pro-cdh topology on schemes introduced in [KS23]. As an application, we give a topos-theoretic interpretation of Weibel's vanishing of negative K-theory and motivic cohomology of Elmanto and Morrow.

Keywords

Cite

@article{arxiv.2409.14295,
  title  = {A pro-cdh topology on formal schemes},
  author = {Shane Kelly and Shuji Saito},
  journal= {arXiv preprint arXiv:2409.14295},
  year   = {2024}
}
R2 v1 2026-06-28T18:52:38.289Z