Towards a higher arithmetic Siegel-Weil formula for unitary groups

Abstract: The classical Siegel-Weil formula relates an integral of a theta function along one classical group H to special values of the Siegel-Eisenstein series on another classical group G. Kudla proposed an arithmetic analogue of it that relates a generating series of algebraic cycles on the Shimura variety for H to the first derivative of the Siegel-Eisenstein series for G, which has become a very active program. We propose to go further in the function field case, relating a generating series of algebraic cycles on the moduli of H-Shtukas with multiple legs to higher derivatives of the Siegel-Eisenstein series for G, when H and G are unitary groups. We prove such a formula for nonsingular Fourier coefficients, relating their higher derivatives to degrees of zero cycles on the moduli of unitary Shtukas. The proof ultimately relies on an argument from Springer theory. This is joint work with Tony Feng and Wei Zhang.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Columbia Automorphic Forms and Arithmetic Seminar