On the vanishing of Relative Negative K-theory

2017/01/31 by Sadhu, Vivek
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1701.09059

Abstract

In this article, we study the relative negative K-groups K_-n(f) of a map f: X → S of schemes. We prove a relative version of the Weibel conjecture i.e. if f: X → S is a smooth affine map of noetherian schemes with dim S=d then K_-n(f)=0 for n> d+1 and the natural map K_-n(f) → K_-n(f × \mathbbA^r) is an isomorphism for all r>0 and n>d. We also prove a vanishing result for relative negative K-groups of a subintegral map.

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