Height pairings on orthogonal Shimura varieties

2017/03/01 by Fabrizio Andreatta, Eyal Z. Goren, Benjamin Howard +1 · 5 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Advanced Mathematical Identities

paper · pdf · doi:10.1112/s0010437x1600779x

Abstract

Let M be the Shimura variety associated to the group of spinor similitudes of a quadratic space over ℚ of signature (n,2) . We prove a conjecture of Bruinier and Yang, relating the arithmetic intersection multiplicities of special divisors and complex multiplication points on M to the central derivatives of certain L -functions. Each such L -function is the Rankin–Selberg convolution associated with a cusp form of half-integral weight n/2+1 , and the weight n/2 theta series of a positive definite quadratic space of rank n . When n=1 the Shimura variety M is a classical quaternionic Shimura curve, and our result is a variant of the Gross–Zagier theorem on heights of Heegner points.

Citations

• Integral canonical models for Spin Shimura varieties

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