2009/03/01 by Benjamin Howard · 10 citations
Mathematics · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Codimension #Complex multiplication #Corollary #Eisenstein series #Elliptic curve #Fourier series #Intersection (aeronautics) #Intersection theory #Mathematical analysis #Mathematics #Modular form #Pure mathematics #Shimura variety #math.NT
paper · pdf · doi:10.1112/s0010437x09003935
published in Compositio Mathematica 145(2), 423-475 (Cambridge University Press)
openalex publication_date 2009/03/01 · arxiv created 2012/02/28 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 and 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 cycle classes constructed by Kudla, Rapoport and Yang. As a corollary we deduce that our intersection multiplicities appear as Fourier coefficients of a Hilbert modular form of half-integral weight.