Deformation theory of the Chow group of zero-cycles

TL;DR

This paper investigates how the Chow group of zero-cycles deforms in smooth schemes over henselian discrete valuation rings, using Bloch's formula and differential forms to establish algebraization results.

Contribution

It introduces new methods involving moving lemmata and Lefschetz theorems for cohomology with differential forms, advancing the understanding of zero-cycle deformations.

Findings

Established algebraization theorem for thickened zero-cycles.

Developed moving lemmata for cohomology groups with differential forms.

Connected deformation theory with cohomological techniques.

Abstract

We study the deformations of the Chow group of zero-cycles of the special fibre of a smooth scheme over a henselian discrete valuation ring. Our main tools are Bloch's formula and differential forms. As a corollary we get an algebraization theorem for thickened zero-cycles previously obtained using idelic techniques. In the course of the proof we develop moving lemmata and Lefschetz theorems for cohomology groups with coefficients in differential forms.