On a canonical class of Green currents for the unit sections of abelian schemes

Author: 

Maillot, V
Rössler, D

Publication Date: 

1 January 2015

Journal: 

Documenta Mathematica

Last Updated: 

2020-02-17T12:04:42.987+00:00

Volume: 

20

page: 

631-668

abstract: 

We show that on any abelian scheme over a complex quasi-projective smooth variety, there is a Green current for the zero-section, which is axiomatically determined up to $\partial$ and $\bar\partial$-exact differential forms. This current generalizes the Siegel functions defined on elliptic curves. We prove generalizations of classical properties of Siegel functions, like distribution relations, limit formulae and reciprocity laws.

Symplectic id: 

745034

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article