2012/08/04 by Matthew Morrow, Morrow, Matthew
Mathematics · #14H20 (Secondary) #19D55 (Primary) 11S70 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.AG #math.KT #msc:11S70 #msc:14H20 #msc:19D55
paper · pdf · doi:10.48550/arxiv.1208.0931
arxiv created 2012/08/04 · openalex publication_date 2012/08/04 · arxiv updated 2012/08/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The first part of this paper introduces an analogue, for one-dimensional, singular, complete local rings, of Gersten's injectivity conjecture for discrete valuation rings. Our main theorem is the verification of this conjecture when the ring is reduced and contains Q, using methods from cyclic/Hochschild homology and Artin-Rees type results due to A. Krishna. The second part of the paper describes the relationship between adele type resolutions of K-theory on a one-dimensional scheme and more classical questions in K-theory such as localisation and descent. In particular, we construct a new resolution of sheafified K-theory, conditionally upon the conjecture.