Pure and Applied Mathematics Quarterly

Volume 16 (2020)

Number 5

Infinitesimal deformation of Deligne cycle class map

Pages: 1707 – 1722

DOI: https://dx.doi.org/10.4310/PAMQ.2020.v16.n5.a12


Sen Yang (School of Mathematics, Southeast University, Nanjing, China; Shing-Tung Yau Center of Southeast University, Southeast University, Nanjing, China; and Yau Mathematical Sciences Center, Tsinghua University, Beijing, China)


In this note, we study the infinitesimal forms of Deligne cycle class maps. As an application, we prove that the infinitesimal form of a conjecture by Beilinson [1] is true.


Chow groups, Milnor $K$-theory, Deligne cohomology, infinitesimal deformation, Abel–Jacobi map

2010 Mathematics Subject Classification


This work was partially supported by the Fundamental Research Funds for the Central Universities.

Received 15 May 2019

Accepted 14 October 2019

Published 17 February 2021