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Derived Representation Theory and the Algebraic K-theory of Fields

We describe the construction which takes as input a profinite group, which when applied the the absolute Galois group of a geometric field F agrees in some cases with the algebraic K-theory of F. We prove that it agrees in the case of a topologically finitely generated abelian absolute Galois group, and conjecture that it agrees for all geometric fields. We also discuss properties of the construction, including relationships with the representation theory of infinite discrete groups.

preprint2008arXivOpen access
Gunnar Carlsson
math.ATmath.AC
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Gunnar Carlsson

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