Vol. 14, No. 4, 2020

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A moving lemma for relative 0-cycles

Amalendu Krishna and Jinhyun Park

Vol. 14 (2020), No. 4, 991–1054
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