Asian Journal of Mathematics

Volume 22 (2018)

Number 3

Special issue in honor of Ngaiming Mok (2 of 3)

Guest Editors: Jun-Muk Hwang, Korea Institute for Advanced Study; Yum-Tong Siu, Harvard University; Wing-Keung To, National University of Singapore; Stephen S.-T. Yau, Tsinghua University; Sai-Kee Yeung, Purdue University

Numerical boundedness on rational equivalences of zero cycles on algebraic varieties with trivial $\mathrm{CH}_0$

Pages: 569 – 576

DOI: https://dx.doi.org/10.4310/AJM.2018.v22.n3.a9

Authors

Shun-Ichi Kimura (Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Japan)

Mao Sheng (School of Mathematical Sciences, University of Science and Technology of China, Hefei, China)

Mingwei Zhang (School of Mathematical Sciences, University of Science and Technology of China, Hefei, China)

Abstract

The main purpose of this article is to show that there exists numerical bound with respect to rational equivalences in some sense. We also prove that finite dimensionality of the zero-dimensional Chow groups are preserved by degeneration.

Keywords

algebraic cycles, rational equivalence

2010 Mathematics Subject Classification

14C25

Full Text (PDF format)

The second- and third-named authors are supported by the National Natural Science Foundation of China (Grant No. 11622109, No. 11626253, No. 11721101), and by the Fundamental Research Funds for the Central Universities.

Received 14 October 2016

Accepted 26 June 2017

Published 8 August 2018