English

A moving lemma for relative $0$-cycles

Algebraic Geometry 2020-06-24 v3 K-Theory and Homology

Abstract

We prove a moving lemma for the additive and ordinary higher Chow groups of relative 00-cycles of regular semi-local kk-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

Cite

@article{arxiv.1806.08045,
  title  = {A moving lemma for relative $0$-cycles},
  author = {Amalendu Krishna and Jinhyun Park},
  journal= {arXiv preprint arXiv:1806.08045},
  year   = {2020}
}

Comments

v1: 42 pages. Evolved from \S 5 to \S 11 of arXiv:1504.08181. A generalization of the remaining part of arXiv:1504.08181 posted as a replacement of arXiv:1504.08181/ v2: 42 pages. Revised / v3: 47 pages. Major revision. A version of it to appear in Algebra & Number Theory. (This is different from the final accepted version, due to copyright reason.)

R2 v1 2026-06-23T02:36:49.082Z