Siqi Yang

mod p Hilbert modular forms

Serre's conjecture tells us that an odd, irreducible mod p Galois representation arises from a mod p modular form. A similar phenomenon for totally real fields and Hilbert modular forms has also been conjectured. In this talk, we'll introduce the definition of Hilbert modular forms as sections of automorphic line bundles on Hilbert modular varieties. We'll also discuss about the liftability from characteristic p to characteristic 0.