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arXiv · 2104.09662

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

Fei Ren
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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.

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Fei Ren. 2021-04-19. Bloch's cycle complex and coherent dualizing complexes in positive characteristic. https://arxiv.org/abs/2104.09662

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