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

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.
Publication status:
Published
Peer review status:
Peer reviewed

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
Publisher:
Documenta Mathematica Publisher's website
Journal:
Documenta Mathematica Journal website
Volume:
20
Pages:
631-668
Publication date:
2015-01-01
Acceptance date:
2014-12-12
ISSN:
1431-0635
Source identifiers:
745034
Keywords:
Pubs id:
pubs:745034
UUID:
uuid:231dc76f-cb35-47b4-a30b-00ab8c5c28c2
Local pid:
pubs:745034
Deposit date:
2018-04-13

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