On the arithmetic Siegel–Weil formula for GSpin Shimura varieties
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222_2022_1106_ReferencePDF.pdf
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Author(s)
Li, Chao
Zhang, Wei
Date Issued
March 16, 2022
Publisher
Springer Berlin Heidelberg
Citation
Li, Chao and Zhang, Wei. 2022. "On the arithmetic Siegel–Weil formula for GSpin Shimura varieties."
Version
Author's final manuscript
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Attribution-NonCommercial-ShareAlike 4.0 International
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DOI of Published Version
https://doi.org/10.1007/s00222-022-01106-z
