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Representations of Galois groups and Algebraic K-theory of fields

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KA2W01 - Algebraic K-theory, motivic cohomology and motivic homotopy theory

We have shown in earlier work that there is a strong relationship between derived completions of representation rings of absolute Galois groups and Milnor K-theory, and that this relationship derives from a spectrum level construction relating a completion of the K-theory spectrum of the category of finite dimensional representations of the absolute Galois group of a field F with  the K-theory spectrum of F. We will describe this relationship and progress toward a proof of the main conjecture, namely that the the completion of the representation theory spectrum is equivalent to the K-theory spectrum of the field.  This is joint work with Roy Joshua. 

This talk is part of the Isaac Newton Institute Seminar Series series.

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