A finiteness theorem for zero cycles over fields of Laurent series (2nd part)

Abstract:

The Chow group of an algebraic variety on a field has behavior analogous to the homology group of topological spaces. These are formed in a similar way to simplicial homology. In this talk, given a smooth and projective scheme $X$ over $k[[t]]$ with $k$ a finite or separably closed field, we present a finiteness theorem relating the 1-cycle Chow group $ CH_{1}(X)$ with the 0-cycle Chow groups $CH_{0}(X_{\eta})$ and $CH_{0}(X_{s})$ that correspond to the generic fiber and closed fiber respectively.