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arXiv · 2409.14295

A pro-cdh topology on formal schemes

Shane Kelly·Shuji Saito
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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.

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Shane Kelly, Shuji Saito. 2024-09-22. A pro-cdh topology on formal schemes. https://arxiv.org/abs/2409.14295

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