Resumen de Complex multiplication cycles and Kudla-Rapoport divisors

Benjamin Howard

• We study the intersections of special cycles on a unitary Shimura variety of signature (n-1,1) and show that the intersection multiplicities of these cycles agree with Fourier coefficients of Eisenstein series. The results are new cases of conjectures of Kudla and suggest a Gross-Zagier theorem for unitary Shimura varieties.