Local fields and extraordinary K-theory
Algebraic Topology
2012-07-24 v2
Abstract
We describe integral lifts K(L), indexed by local fields L of degree n = [L:\Q_p], of the extraordinary cohomology theories K(n), and apply the generalized character theory of Hopkins, Kuhn and Ravenel to identify K(L)(BG) \otimes \Q$, for a finite group G, as a ring of functions on a certain scheme \frak C_LG \'etale over L, whose points are conjugacy classes of homomorphisms from the valuation ring of L to G. When L is \Q_p this specializes to a classical theorem of Artin and Atiyah.
Cite
@article{arxiv.1207.4011,
title = {Local fields and extraordinary K-theory},
author = {Jack Morava},
journal= {arXiv preprint arXiv:1207.4011},
year = {2012}
}
Comments
Small remarks, eg re Tate cohomology, references etc, added. A Seminaire Bourbaki report (from an alternate universe). Thanks to many friends and colleagues