5 janvier 2021

Zhiwei Yun (M.I.T.)
Towards a higher arithmetic Siegel-Weil formula for unitary groups

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Lieu : Séminaire en ligne

Résumé : The classical Siegel-Weil formula relates an integral of a
theta function along one classical group H to values of the
Siegel-Eisenstein series on another classical group G. Kudla and
Rapoport proposed an arithmetic analogue of it that relates the
intersection number of certain cycles on the Shimura variety for H to
the Fourier coefficients of the first derivative of the
Siegel-Eisenstein series for G. We propose to go further in the
function field case, relating the intersection number of cycles on the
moduli of Shtukas for H to the Fourier coefficients of higher
derivatives of the Siegel-Eisenstein series for G. We prove such a
formula for non-degenerate Fourier coefficients when H and G are
unitary groups. Somewhat unexpectedly, the proof ultimately relies on
an argument from Springer theory. This is joint work with Tony Feng
and Wei Zhang.

Towards a higher arithmetic Siegel-Weil formula for unitary groups  Version PDF