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

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.

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The author is supported by the DFG through CRC 1085 Higher Invariants (Universität Regensburg).

Received 26 September 2017

Accepted 29 August 2018

Published 12 August 2019