Ampleness criterion of automorphic line bundles on Hilbert modular varieties
Deding Yang
2023-06-02 10:30-11:30
MCM110
Speaker: Deding Yang (Peking University)Time: 10:30-11:30 June 2, 2023 (Friday)
Place: MCM110
Title: Ampleness criterion of automorphic line bundles on Hilbert modular varieties
Abstract: Let F be a totally real field in which p is unramfied and let S denote the integral model of the Hilbert modular variety with good reduction at p. Consider the usual modular line bundle L over S. On the generic fiber, it is well known that L is ample if and only if all the coefficients are positive. On the special fiber, [Tian-Xiao] conjectured L is ample if an only if the coefficients satisfy certain inequalities. They formulated a criterion and proved the necessity using a description of certain Goren--Oort strata. In this talk, we recall their results and prove the sufficiency of this ampleness criterion.
