### The Tate-Thomason conjecture, by Masana Harada

[The paper has been withdrawn by the author, July 22, 2010.]

[The original paper, submitted Dec 3, 2008, revised Jan 30, 2009, has been
revised March 10, 2009, with this comment:] This is an update to #919. The
treatment of the torsion free term was not right.

This is an application of "Higher K-theory of algebraic curves", #915 of the
archive.

In this paper we will prove that the co-invariant subspace of topological Adams
operations on E(1)-homology of algebraic K-theory spectra E(1)K(X) associaterd
to algebraic varieties X over finite fields does not contain any divisible
subgroup. (E(1) is the Adams factor of topological periodic complex
K-theory.)

It implies a conjecture of R.W.Thomason that there does not exist any
divisible subgroup on the (-1)-th E(1)-localized K-theory of projective smooth
varieties over finite fields.

Masana Harada <harada@math.kyoto-u.ac.jp>