Abstract

In this paper, we obtain an explicit arithmetic intersection formula on a Hilbert modular surface between the diagonal embedding of the modular curve and a CM cycle associated to a non-biquadratic CM quartic field. This confirms a special case of the author's conjecture with Bruinier, and is a generalization of the beautiful factorization formula of Gross and Zagier on singular moduli. As an application, we proved the first nontrivial non-abelian Chowla-Selberg formula, a special case of Colmez conjecture.

pdf

Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 1275-1309
Launched on MUSE
2010-10-16
Open Access
No
Archive Status
Back To Top

This website uses cookies to ensure you get the best experience on our website. Without cookies your experience may not be seamless.