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LOCAL BORCHERDS PRODUCTS FOR UNITARY GROUPS

Part of: Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  27 October 2017

ERIC HOFMANN
ERIC HOFMANN*
Affiliation:
Mathematisches Institut, Universität Heidelberg, Im Neuenheimer Feld 205, D-69120 Heidelberg, Germany email hofmann@mathi.uni-heidelberg.de
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Abstract

For the modular variety attached to an arithmetic subgroup of an indefinite unitary group of signature $(1,n+1)$, with $n\geqslant 1$, we study Heegner divisors in the local Picard group over a boundary component of a compactification. For this purpose, we introduce local Borcherds products. We obtain a precise criterion for local Heegner divisors to be torsion elements in the Picard group, and further, as an application, we show that the obstructions to a local Heegner divisor being a torsion element can be described by certain spaces of vector-valued elliptic cusp forms, transforming under a Weil representation.

MSC classification

Primary: 11F27: Theta series; Weil representation; theta correspondences 11F55: Other groups and their modular and automorphic forms (several variables) 11G18: Arithmetic aspects of modular and Shimura varieties 11G35: Varieties over global fields
Type
Article
Information
Nagoya Mathematical Journal , Volume 234 , June 2019 , pp. 139 - 169
Copyright
© 2017 Foundation Nagoya Mathematical Journal  

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