Algebraization for zero-cycles and the -adic cycle class map

Abstract

Using an idelic argument and assuming the Gersten conjecture for Milnor K-theory, we show that the restriction map from the Chow group of one-cycles on a smooth projective scheme over a henselian local ring to a pro-system of thickened zero-cycles is surjective. We relate this restriction map to the p-adic cycle class map.