A geometric reformulation of the representational assembly conjecture for the K-theory of fields with pro-l absolute Galois group

Abstract

In this paper we prove a result which establishes an equivalence between the representational assembly conjecture proposed by the author and a rigidity question, in the case of Galois groups which are pro-l groups. In additional work with R. Joshua, we will confirm the validity of this rigidity conjecture, thereby proving the conjecture in the case of a pro-l absolute Galois group.