K-theory and geometric Galois representations

Wieslawa Niziol, University of Utah, niziol@math.utah.edu

Galois representations arising from p-adic etale cohomology of algebraic varietes over local fields of mixed characteristic have certain particular properties. We will show this in the case of projective varieties with semi-stable reduction (the Semi-stable Conjecture of Jannsen and Fontaine proved earlier by Tsuji and Faltings). Our argument is based on Thomason's comparison theorem between algebraic and etale K-theories.