A genus two arithmetic Siegel-Weil formula on 𝑋₀(𝑁)

Sankaran, Siddarth; Shi, Yousheng; Yang, Tonghai

doi:10.1090/tran/8843

A genus two arithmetic Siegel-Weil formula on $X_0(N)$
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by Siddarth Sankaran, Yousheng Shi and Tonghai Yang;

Trans. Amer. Math. Soc. 376 (2023), 3995-4041

DOI: https://doi.org/10.1090/tran/8843

Published electronically: March 21, 2023

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Abstract:

We define a family of arithmetic zero cycles in the arithmetic Chow group of a modular curve $X_0(N)$, for $N>3$ odd and squarefree, and identify the arithmetic degrees of these cycles as $q$-coefficients of the central derivative of a Siegel Eisenstein series of genus two. This parallels work of Kudla-Rapoport-Yang for Shimura curves.

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