#### 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