On Two Geometric Theta Lifts

2002/12/20 by Jan Hendrik Bruinier, Jens Funke, Bruinier, Jan Hendrik +1 · 6 citations
Mathematics · #11F55 #14C25 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11F55 #msc:14C25

paper · pdf · doi:10.48550/arxiv.math/0212286

35 pages

arxiv created 2003/03/14 · arxiv updated 2009/11/30

Abstract

The theta correspondence has been an important tool in studying cycles in locally symmetric spaces of orthogonal type. In this paper, we establish for O(p,2) an adjointness result between Borcherds' singular theta lift and the Kudla-Millson theta lift. We extend this result to arbitrary signature by introducing a new Borcherds lift for O(p,q). On the geometric side, this lift can be interpreted as a differential character in the sense of Cheeger and Simons.

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