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

Let X X be a separated scheme of dimension d d of finite type over a perfect field k k of positive characteristic p p . In this work, we show that Bloch’s cycle complex Z X c \mathbb {Z}^c_X of zero cycles mod p n 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 p^n coefficients for singular varieties.