On the arithmetic Siegel--Weil formula for GSpin Shimura varieties

Chao Li; Wei Zhang

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arXiv · 2106.15038

On the arithmetic Siegel--Weil formula for GSpin Shimura varieties

Chao Li·Wei Zhang

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Abstract

We formulate and prove a local arithmetic Siegel--Weil formula for GSpin Rapoport--Zink spaces, which is a precise identity between the arithmetic intersection numbers of special cycles on GSpin Rapoport--Zink spaces and the derivatives of local representation densities of quadratic forms. As a first application, we prove a semi-global arithmetic Siegel--Weil formula as conjectured by Kudla, which relates the arithmetic intersection numbers of special cycles on GSpin Shimura varieties at a place of good reduction and the central derivatives of nonsingular Fourier coefficients of incoherent Siegel Eisenstein series.

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Chao Li, Wei Zhang. 2021-06-29. On the arithmetic Siegel--Weil formula for GSpin Shimura varieties. https://arxiv.org/abs/2106.15038

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