#### 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
##### Abstract

We introduce a regularized theta lift for reductive dual pairs $\left({Sp}_{4},O\left(V\right)\right)$, 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 $GSpin\left(V\right)$; 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.

##### Keywords
Shimura varieties, theta series, Weil representation
##### Mathematical Subject Classification 2010
Primary: 11F27
Secondary: 11F67, 11G18, 14G35