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In this paper we prove a result which establishes an equivalence between therepresentational assembly conjecture proposed by the author and a rigidityquestion, in the case of Galois groups which are pro-l groups. In additionalwork 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.

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