A restriction isomorphism for cycles of relative dimension zero

TL;DR

This paper investigates a restriction map related to zero-cycles on regular projective schemes over henselian DVRs, extending previous work to broader residue fields, and provides new insights into the cohomological Chow group structure.

Contribution

It generalizes the restriction isomorphism for zero-cycle Chow groups to cases with perfect residue fields, broadening the applicability of Saito--Sato's results.

Findings

Established a restriction isomorphism for cohomological zero-cycle Chow groups

Extended Saito--Sato's results to perfect residue fields

Provided new tools for studying zero-cycles in algebraic geometry

Abstract

We study the restriction map to the closed fiber of a regular projective scheme over an excellent henselian discrete valuation ring, for a cohomological version of the Chow group of relative zero-cycles. Our main result extends the work of Saito--Sato to general perfect residue fields.