2010/03/16 by Gunnar Carlsson, Carlsson, Gunnar
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1003.3062
openalex publication_date 2010/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns our earlier conjecture about the equivalence of a derived completion construction applied to the representation spectrum of the absolute Galois group of a geometric field is equivalent to the algebraic K-theory of the field. We prove that the p-adic version of the derived completion construction can be interpreted as the K-theory of a certain pro-scheme over an algebraically closed field contained within the field. In order to make this construction, we use a special property of absolute Galois groups of geometric field, namely that of total torsion freeness, and the paper also contains some poperties of the representation theory of such groups.