Arithmetic Intersection and a conjecture of Lauter

Опубликовано 6 сентября 2016, 18:11

Motivated by her joint work with H. Cohn on genus two curve crypotosystem, Lauter gave a very inspiring conjecture on the CM value of Igusa invariants. They need to compute these values to construct `good' genus two curves. This conjecture led to study of arithmetic intersection on an arithmetic 3-fold (Hilbert modular surface). Recently, I proved an arithmetic intersection formula, which leads to proof of Lauter's conjecture. The formula also leads to the first non-abelian generalization of the celebrated Chowla-Selberg formula.