2017/10/01 by Chris Skalit, Skalit, C. · 1 citation
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Graph theory and applications #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1710.00303
openalex publication_date 2017/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that if X → Y is a (geometrically) regular morphism of Noetherian schemes, then from a Nisnevich-local perspective, the Gersten complex for Quillen K-theory on X becomes acyclic in degrees beyond the Krull dimension of Y. Using our methods, we also reduce the general Gersten conjecture for regular, unramified local rings to the case of a discrete valuation ring which is essentially smooth over ℤ. We apply our results to the the theory of algebraic cycles --- globally to obtain relative versions of Bloch's Formula and locally to address the Claborn-Fossum Conjecture concerning the vanishing of Chow groups for regular local rings.