Heights of Kudla–Rapoport divisors and derivatives of L-functions
نویسندگان
چکیده
We study special cycles on integral models of Shimura varieties associated with unitary similitude groups of signature (n−1, 1). We construct an arithmetic theta lift from harmonic Maass forms of weight 2 − n to the arithmetic Chow group of the integral model of a unitary Shimura variety, by associating to a harmonic Maass form f a linear combination of Kudla– Rapoport divisors, equipped with the Green function given by the regularized theta lift of f . Our main result is an equality of two complex numbers: (1) the height pairing of the arithmetic theta lift of f against a CM cycle, and (2) the central derivative of the convolution L-function of a weight n cusp form (depending on f ) and the theta function of a positive definite hermitian lattice J. H. Bruinier is partially supported by DFG Grant BR-2163/4-1. B. Howard is partially supported by NSF Grant DMS-1201480. T. Yang is partially supported by a NSF Grant DMS-1200380 and a Chinese grant. J. H. Bruinier (B) Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany e-mail: [email protected] B. Howard Department of Mathematics, Boston College, 140 Commonwealth Ave, Chestnut Hill, MA 02467, USA e-mail: [email protected] T. Yang Department of Mathematics, University of Wisconsin Madison, Van Vleck Hall, Madison, WI 53706, USA e-mail: [email protected]
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