Co-rank 1 Arithmetic Siegel–Weil

Abstract: I will introduce my recent work on an arithmetic Siegel–Weil formula for Kudla–Rapoport $1$-cycles on integral models of some unitary Shimura varieties. This formula implies that degrees of Kudla–Rapoport arithmetic special $1$-cycles are encoded in the first derivatives of unitary Eisenstein series Fourier coefficients. In the simplest case, this can be rephrased in terms of Faltings heights of Hecke translates of CM elliptic curves, and the classical weight $2$ Eisenstein series.

The key input is a new local limiting method which relates (a) degrees of local special 0-cycles and (b) local contributions to heights of special $1$-cycles.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper )

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MIT number theory seminar

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