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The Gross-Zagier formula on singular moduli for Shimura curves

Number Theory 2025-09-16 v1 Algebraic Geometry

Abstract

The Gross-Zagier formula on singular moduli can be seen as a calculation of the intersection multiplicity of two CM divisors on the integral model of a modular curve. We prove a generalization of this result to a Shimura curve.

Keywords

Cite

@article{arxiv.2509.11553,
  title  = {The Gross-Zagier formula on singular moduli for Shimura curves},
  author = {Andrew Phillips},
  journal= {arXiv preprint arXiv:2509.11553},
  year   = {2025}
}

Comments

33 pages; comments welcome