On a canonical class of Green currents for the unit sections of abelian schemes
- 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.
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- This is the publisher's version of the article. The final version is available online from Documenta Mathematica at: https://www.math.uni-bielefeld.de/documenta/vol-20/17.html
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