Number Theory Seminar

The intersection theory of special cycles on Shimura varieties of unitary and orthogonal type are known to relate to Fourier coeffcients of Eisenstein series. Passing to integral models and equipping the special cycles with extra analytic data, their Arakelov intersection theory is in general expected, and in many cases known, to correspond to Fourier coefficients of derivatives of Eisenstein series. These phenomena are typically studied with simplifying assumptions on the signature types of the hermitian/quadratic spaces from which the Shimura variety and the special cycles arise. I will report on work in progress involving a simple case where this signature restriction is lifted. One obtains a larger family of cycles and a richer intersection theory at the cost of non-compactness and the need to regularize the Siegel-Weil formula.