  We study Bloch-Ogus theory and the Gersten conjecture for homology theories
with duality satisfying certain properties, in particular for \'etale
cohomology with finite coefficients coprime to the residue characteristic of
the base, for smooth and semi-stable schemes in mixed characteristic. We prove
the Gersten conjecture in the smooth case and prove a special case in the
semi-stable situation. As a corollary of the smooth case we obtain the
surjectivity of the Galois symbol map for arbitrary local rings over an
excellent discrete valuation ring.
