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Regularized theta lifts and (1,1)-currents on GSpin Shimura varieties

Garcia, L; (2016) Regularized theta lifts and (1,1)-currents on GSpin Shimura varieties. Algebra & Number Theory , 10 (3) pp. 597-644. 10.2140/ant.2016.10.597. Green open access

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Abstract

We introduce a regularized theta lift for reductive dual pairs ( Sp 4 , O ( V ) ) , for V a quadratic vector space over a totally real number field. The lift takes values in the space of (1,1)-currents on the Shimura variety attached to GSpin ( V ) ; we show its values are cohomologous to currents given by integration on special divisors against automorphic Green functions. A later paper will show how to evaluate the new lift on differential forms obtained as usual (nonregularized) theta lifts.

Type: Article
Title: Regularized theta lifts and (1,1)-currents on GSpin Shimura varieties
Open access status: An open access version is available from UCL Discovery
DOI: 10.2140/ant.2016.10.597
Publisher version: https://doi.org/10.2140/ant.2016.10.597
Language: English
Additional information: First published in Algebra & Number Theory in Vol. 10 (2016), No. 3, published by Mathematical Sciences Publishers. This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Shimura varieties, theta series, Weil representation
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10086961
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