Notices of the International Consortium of Chinese Mathematicians

Volume 8 (2020)

Number 2

On the periods of abelian varieties

Pages: 10 – 18



Benedict H. Gross (Leverett Professor of Mathematics, Emeritus, Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)


In this expository paper, we review the formula of Chowla and Selberg for the periods of elliptic curves with complex multiplication, and discuss two methods of proof. One uses Kronecker’s limit formula and the other uses the geometry of a family of abelian varieties. We discuss a generalization of this formula, which was proposed by Colmez, as well as some explicit Hodge cycles which appear in the geometric proof.

Published 14 April 2021