Damian Roessler: On a canonical class of Green currents for the unit sections of 
abelian schemes
<br><br>
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.