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

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.