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A procdh topology

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arxiv 2401.02699 v1 pith:NC7C4LII submitted 2024-01-05 math.AG math.KT

Shane Kelly , Shuji Saito This is my paper · ORCID
classification math.AGmath.KT
keywords procdhcohomologymotivicsheafificationtheoryadmitsapplicationarticle
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abstract

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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Weibel vanishing and the projective bundle formula for mixed characteristic motivic cohomology

    math.AG 2025-07 conditional novelty 7.0 of 10

    Mixed characteristic motivic cohomology satisfies Weibel vanishing, the projective bundle formula, comparison to Milnor K-theory, and pro cdh descent.

  2. On the motivic cohomology of some singular rings

    math.AG 2026-08 conditional novelty 6.0 of 10

    The non-A1-invariant motivic cohomology groups are now explicitly computed for finite chain rings, truncated polynomial rings, perfect and semiperfect rings, valuation rings, and commutative C*-algebras.

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