We study the deformations of the Chow group of zerocycles 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.

中文翻译：

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零周期周群的变形理论

我们研究了在Henselian离散评估环上的光滑方案的特殊纤维的零周期Chow群的变形。我们的主要工具是Bloch的公式和微分形式。作为推论，我们得到了以前使用理想技术获得的增零循环的代数定理。在证明的过程中，我们为系数为微分形式的同调群开发了移动引理和Lefschetz定理。