A procdh topology

Fuente: arXiv
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Main Authors: Kelly, Shane, Saito, Shuji
Format: Preprint
Published: 2024
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author Kelly, Shane
Saito, Shuji
author_facet Kelly, Shane
Saito, Shuji
contents In this article we propose a definition of a procdh topos. We show that it encodes procdh excision, has bounded homotopy dimension and therefore is hypercomplete and admits a conservative family of fibre functors. We also describe the local rings. As an application, we show that nonconnective $K$-theory is the procdh sheafification of connective $K$-theory, and that the motivic cohomology recently proposed by Elmanto and Morrow is the procdh sheafification of Voevodsky's motivic cohomology.
format Preprint
id arxiv_https___arxiv_org_abs_2401_02699
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A procdh topology
Kelly, Shane
Saito, Shuji
Algebraic Geometry
K-Theory and Homology
In this article we propose a definition of a procdh topos. We show that it encodes procdh excision, has bounded homotopy dimension and therefore is hypercomplete and admits a conservative family of fibre functors. We also describe the local rings. As an application, we show that nonconnective $K$-theory is the procdh sheafification of connective $K$-theory, and that the motivic cohomology recently proposed by Elmanto and Morrow is the procdh sheafification of Voevodsky's motivic cohomology.
title A procdh topology
topic Algebraic Geometry
K-Theory and Homology
url https://arxiv.org/abs/2401.02699