arXiv:1007.0427 The Tate Thomason Conjecture from arXiv Front: math.AT by Marcelo Gomez Morteo We prove the Tate Thomason conjecture using K(l) localized spectra where K(1)=E(1)/l where l is an odd prime and E(1) is the complex topology spectrum. Fundamental to our proof is Theorem 2.1 below, where we show that certain K(1) localized spectra are E(1)^ module spectra.We also make fundamental use of the notion of etale and topological K Theory and its relation to algebraic K theory through Thomason’s descent theorem.
nLab page on Tate-Thomason conjecture