Eyal Z. Goren

Lectures on Hilbert modular varieties and modular forms

Introduction Tori and abelian varieties Complex abelian varieties with real multiplication and Hilbert modular forms Abelian varieties with real multiplication over general fields

Hasse invariants for Hilbert modular varieties

p

On certain reduction problems concerning Abelian surfaces.

-adic elliptic modular forms

Canonical Subgroups over Hilbert Modular Varieties

p

Geometry of Hilbert modular varieties over totally ramified primes

-adic Hilbert modular forms Deformation theory of abelian varieties Group schemes Calculating with cusps Bibliography Notation index Index.

Evil Primes and Superspecial Moduli

AbstractGiven a totally real fieldL of degreeg, we constructg Hasse invariants on Hilbert modular varieties in characteristicp and characterize their divisors. We show that these divisors give the type stratification defined by the action of

A theta operator on Picard modular forms modulo an inert prime

\mathcal{O}_L

Hilbert modular forms : mod p and p-adic aspects

on theαp-elementary subgroup. Under certain conditions, involving special values of zeta functions, the product of these Hasse invariants is the reduction of an Eisenstein series of weightp−1