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arXiv · 2206.05823

A genus two arithmetic Siegel-Weil formula on X_0(N)

Siddarth Sankaran·Yousheng Shi·Tonghai Yang
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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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Siddarth Sankaran, Yousheng Shi, Tonghai Yang. 2022-06-12. A genus two arithmetic Siegel-Weil formula on X_0(N). https://arxiv.org/abs/2206.05823

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