p-primary torsion part of Bloch's cycle complex from Grothendieck's coherent duality point of view

Abstract

Let X be a separated scheme of finite type over k with k being a perfect field of positive characteristic p. In this thesis we define a complex K_{n,X,log} via Grothendieck’s duality theory of coherent sheaves following [Kat87] and build up a quasi-isomorphism from the Kato-Moser complex of logarithmic de Rham-Witt sheaves \tilde \nu_{n,X} to K_{n,X,log} for the etale topology, and also for the Zariski topology under the extra assumption k =\bar k. Combined with Zhong’s quasi-isomorphism from Bloch’s cycle complex Z^c_X to \tilde \nu_{n,X} [Zho14, 2.16], we deduce certain vanishing, etale descent properties as well as invariance under rational resolutions for higher Chow groups of 0-cycles with Z/p^n-coefficients.