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arXiv · 1008.1854

Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height

Tonghai Yang
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Abstract

In this paper, we prove an explicit arithmetic intersection formula between arithmetic Hirzebruch-Zagier divisors and arithmetic CM cycles in a Hilbert modular surface over $\mathbb Z$. As applications, we obtain the first `non-abelian' Chowla-Selberg formula, which is a special case of Colmez's conjecture; an explicit arithmetic intersection formula between arithmetic Humbert surfaces and CM cycles in the arithmetic Siegel modular variety of genus two; Lauter's conjecture about the denominators of CM values of Igusa invariants; and a result about bad reductions of CM genus two curves.

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Tonghai Yang. 2010-08-11. Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height. https://arxiv.org/abs/1008.1854

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