The Gross-Zagier formula on singular moduli for Shimura curves
arXiv:2509.11553
summary
The paper extends the Gross‑Zagier formula for singular moduli—originally describing intersection multiplicities of CM divisors on modular curves—to the setting of Shimura curves.
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.
Corrections made; additional details added in many proofs
Topics & keywords
#gross-zagier formula#singular moduli#shimura curves#cm divisors#intersection theory#arithmetic geometryintersection multiplicityCM pointsintegral modelmodular curveShimura curveGross-Zagier formula