A genus two arithmetic Siegel-Weil formula on X_0(N)
Number Theory
2022-06-14 v1 Algebraic Geometry
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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Cite
@article{arxiv.2206.05823,
title = {A genus two arithmetic Siegel-Weil formula on X_0(N)},
author = {Siddarth Sankaran and Yousheng Shi and Tonghai Yang},
journal= {arXiv preprint arXiv:2206.05823},
year = {2022}
}
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43 pages