A restriction isomorphism for cycles of relative dimension zero
I will report on a joint work with Moritz Kerz and Hélène Esnault on the
Chow group of 1-cycles of a regular projective scheme over an excellent
henselian discrete valuation ring. We study a restriction map from this
group to a cohomological version of the Chow group of 0-cycles on the
special fiber. Our main result extends to general perfect residue fields
the work of Saito and Sato on the étale cycle class map for 1-cycles on
regular projective schemes over the ring of integers of a p-adic field.