A moving lemma for relative 0-cycles

Krishna, Amalendu; Park, Jinhyun

doi:10.2140/ant.2020.14.991

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A moving lemma for relative 0-cycles

Amalendu Krishna and Jinhyun Park

Vol. 14 (2020), No. 4, 991–1054

DOI: 10.2140/ant.2020.14.991

Abstract

We prove a moving lemma for the additive and ordinary higher Chow groups of relative $0$ -cycles of regular semilocal $k$ -schemes essentially of finite type over an infinite perfect field. From this, we show that the cycle classes can be represented by cycles that possess certain finiteness, surjectivity, and smoothness properties. It plays a key role in showing that the crystalline cohomology of smooth varieties can be expressed in terms of algebraic cycles.

Keywords

algebraic cycles, moving lemma, higher Chow group, additive higher Chow group, linear projection, Grassmannian

Mathematical Subject Classification 2010

Primary: 14C25

Secondary: 14F42, 19E15

Milestones

Received: 13 April 2019

Revised: 18 November 2019

Accepted: 16 December 2019

Published: 21 June 2020

Authors

Amalendu Krishna
School of Mathematics Tata Institute of Fundamental Research Mumbai India

Jinhyun Park
Department of Mathematical Sciences KAIST Daejeon South Korea

Vol. 14, No. 4, 2020