Derived representation theory and the algebraic K-theory of fields

作者：Carlsson Gunnar E^*

来源：Journal of Topology, 2011, 4(3): 543-572.

DOI：10.1112/jtopol/jtr013

In this paper, we prove a conjecture on the relationship of the algebraic K-theory of a field F, with abelian separable Galois group G(F), containing an algebraically closed subfield with the K-theory of the category of finite-dimensional continuous linear representations of G(F) in an algebraically closed field. The connection is achieved through the use of a certain derived completion construction defined for commutative ring spectra. The paper proposes that the conjecture should hold for non-abelian separable Galois groups.

• 出版日期2011