Bonn Topology Group - Abstracts

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Talk

Michael Groechenig (Imperial College, London): The K-theory of Tate objects (13/01/2015)

Abstract

Abstract Tate objects in exact categories generalise Lefschetz's linearly locally compact vector spaces. The simplest non-trivial example is the vector space of formal Laurent series k((t)) with the t-adic topology. The K-theory space of the exact category of Tate objects can be shown to be a delooping of the K-theory of the original exact category, as shown by Saito. Moreover the two spaces can be compared by a construction reminiscent of Kapranov's determinantal theories. As an application of this theory we give a K-theoretic treatment of higher-dimensional analogues of Contou-Carrère symbols, and use this viewpoint to establish reciprocity laws for those symbols. This is joint work with O. Bräunling and J. Wolfson.

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