Deformation theory of the Chow group of zero-cycles

Morten Lüders

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arXiv · 1810.01347

Deformation theory of the Chow group of zero-cycles

Morten Lüders

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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.

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Morten Lüders. 2018-10-02. Deformation theory of the Chow group of zero-cycles. https://arxiv.org/abs/1810.01347

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