The relative form of Gersten’s conjecture for power series over a complete discrete valuation ring

Abstract

A relative form of Gersten’s Conjecture is established for a ring of formal power series over a complete discrete valuation ring. The main corollaries are that the absolute version of Gersten’s Conjecture is valid for such a ring if it is valid for arbitrary discrete valuation rings, and, consequently, that the conjecture is true for such a ring if we use K K -theory with finite coefficients of order prime to the characteristic of the residue field.