Arithmetic intersection on a Hilbert modular surface and the Faltings height
Arithmetic intersection on a Hilbert modular surface and the Faltings height
In this paper, we prove an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles on a Hilbert modular surface over $\mathbb{Z}$. As applications, we obtain the first ānon-abelianā Chowla-Selberg formula, which is a special case of Colmezās conjecture; an explicit arithmetic intersection formula between arithmetic Humbert ā¦