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.
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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 |
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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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