Localization theorem for higher arithmetic K-theory

Abstract

Quillen's localization theorem is well known as a fundamental theorem in the study of algebraic K-theory. In this paper, we present its arithmetic analogue for the equivariant K-theory of arithmetic schemes, which are endowed with an action of certain diagonalisable group scheme. This equivariant arithmetic K-theory is defined by means of a natural extension of Burgos-Wang's simplicial description of Beilinson's regulator map to the equivariant case. As a byproduct of this work, we give an analytic refinement of the Riemann-Roch theorem for higher equivariant algebraic K-theory. And as an application, we prove a higher arithmetic concentration theorem which generalizes Thomason's corresponding result in purely algebraic case to the context of Arakelov geometry.