On the vanishing of relative negative K-theory

Abstract

In this paper, we study the relative negative [Formula: see text]-groups [Formula: see text] of a map [Formula: see text] of schemes. We prove a relative version of Weibel’s conjecture; i.e. if [Formula: see text] is a smooth affine map of Noetherian schemes with [Formula: see text], then [Formula: see text] for [Formula: see text] and the natural map [Formula: see text] is an isomorphism for all [Formula: see text] and [Formula: see text] We also prove a vanishing result for relative negative [Formula: see text]-groups of a subintegral map.