Abstract
Given 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\(\mathcal{O}_L \) 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
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