Vol. 10, No. 3, 2016

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

Luis E. Garcia

Vol. 10 (2016), No. 3, 597–644

We introduce a regularized theta lift for reductive dual pairs (Sp4,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.

Shimura varieties, theta series, Weil representation
Mathematical Subject Classification 2010
Primary: 11F27
Secondary: 11F67, 11G18, 14G35
Received: 8 May 2015
Revised: 9 December 2015
Accepted: 4 February 2016
Published: 12 June 2016
Luis E. Garcia
Department of Mathematics, South Kensington Campus
Imperial College London
United Kingdom
Department of Mathematics
University of Toronto
40 St. George Street, BA 6290
Toronto, ON M5S 2E4