Benedict H Gross
Published 2020-05-08Version 1
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.
Duality for cohomology of curves with coefficients in abelian varieties
Endomorphisms of abelian varieties, cyclotomic extensions and Lie algebras
Torsion points and height jumping in higher-dimensional families of abelian varieties
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