On the Negative K-theory of Singular Varieties

2013/06/16 by Shih, Justin
#19D35 #19E08 #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1306.3688

Abstract

Let X be an n-dimensional variety over a field k of characteristic zero, regular in codimension 1 with singular locus Z. In this paper we study the negative K-theory of X, showing that when Z is sufficiently nice, K_1-n(X) is an extension of KH_1-n(X) by a finite dimensional vector space, which we compute explicitly. We also show that KH_1-n(X) almost has a geometric structure. Specifically, we give an explicit 1-motive [L → G] and a map G(k) → KH_1-n(X) whose kernel and cokernel are finitely generated abelian groups.

Related

• Negative K-theory and Hodge theory
• Zero cycles on singular varieties and their desingularisations
• Descent, Motives and K-theory
• On the new theory of 1-motives
• Infinitesimal Theory of Chow Groups via K-theory, Cyclic Homology and the Relative Chern Character