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June 2013 Arithmetic intersection on a Hilbert modular surface and the Faltings height
Tonghai Yang
Asian J. Math. 17(2): 335-382 (June 2013).

Abstract

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 ‘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 reduction of CM genus two curves.

Citation

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Tonghai Yang. "Arithmetic intersection on a Hilbert modular surface and the Faltings height." Asian J. Math. 17 (2) 335 - 382, June 2013.

Information

Published: June 2013
First available in Project Euclid: 8 November 2013

Subjects:
Primary: 11F41, 11G15, 14K22

Rights: Copyright © 2013 International Press of Boston

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Vol.17 • No. 2 • June 2013
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