Number Theory Seminar

A new proof of the Arithmetic Siegel--Weil formula

Yu Luo, PhD Candidate, Department of Mathematics, University of Wisconsin-Madison,

The arithmetic Siegel--Weil formula establishes a profound connection between intersection numbers in Shimura varieties and the Fourier coefficients of central derivatives of Eisenstein series. This result was proven by C. Li and W. Zhang in 2022 using local methods. In this talk, I will present a new proof of the formula that uses the local-global compatibility and the modularity of generating series of special divisors.

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