Oriented Chow groups, Hermitian K-theory and the Gersten conjecture

Abstract

We show that the oriented Chow groups of Barge-Morel appear in the E-2-term of the coniveau spectral sequence for Hermitian K-theory. This includes a localization theorem and the Gersten conjecture (over infinite base fields) for Hermitian K-theory. We also discuss the conjectural relationship between oriented and higher oriented Chow groups and Levine's homotopy coniveau spectral sequence when applied to Hermitian K-theory.