Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height

Details Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height

2010-08-11

arxiv.org/abs/1008.1854v1

Mathematics

Number Theory

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Arithmetic Intersection on a Hilbert Modular Surface and the Faltings Height will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-479840