Intersection theory on Shimura surfaces

Abstract

Kudla has proposed a general program to relate arithmetic intersection multiplicities of special cycles on Shimura varieties to Fourier coefficients of Eisenstein series. The lowest dimensional case, in which one intersects two codimension one cycles on the integral model of a Shimura curve, has been completed by Kudla-Rapoport-Yang. In the present paper we prove results in a higher dimensional setting. On the integral model of a Shimura surface we consider the intersection of a Shimura curve with a codimension two cycle of complex multiplication points, and relate the intersection to certain cycles classes constructed by Kudla-Rapoport-Yang. As a corollary we deduce that our intersection multiplicities appear as Fourier coefficients of a Hilbert modular form of half-integral weight.

References in corpus (1)

• Intersection theory on Shimura surfaces II

Cited by in corpus (4)

• Unitary cycles on Shimura curves and the Shimura lift II
• Intersection theory on Shimura surfaces II
• Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height
• Deforming endomorphisms of supersingular Barsotti-Tate groups