Algebra, Geometry & Number Theory Seminar

This talk is based on a series of three papers on the modular heights of unitary Shimura varieties. We prove a formula expressing the modular height of a unitary Shimura variety over a CM number field in terms of the logarithmic derivative of the Hecke LL-function associated with the CM extension. The main idea is to compare the holomorphic projection of the derivative of a mixed Eisenstein-theta series with the arithmetic degree of a generating series of divisors on unitary Shimura varieties.