Bloch's cycle complex and coherent dualizing complexes in positive characteristic

Abstract

Let $X$ be a separated scheme of dimension $d$ of finite type over a perfect field $k$ of positive characteristic $p$. In this work, we show that Bloch's cycle complex $\mathbb{Z}^c_X$ of zero cycles mod $p^n$ is quasi-isomorphic to the Cartier operator fixed part of a certain dualizing complex from coherent duality theory. From this we obtain new vanishing results for the higher Chow groups of zero cycles with mod $p^n$ coefficients for singular varieties.