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Hasse invariants for Hilbert modular varieties. (English) Zbl 1066.11018
Summary: Given a totally real field \(L\) of degree \(g\), we construct \(g\) Hasse invariants on Hilbert modular varieties in characteristic \(p\) and characterize their divisors. We show that these divisors give the type stratification defined by the action of \({\mathcal 0}_L\) on the \(\alpha_p\)-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 weight \(p-1\).

MSC:
11F41 Automorphic forms on \(\mbox{GL}(2)\); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces
11G18 Arithmetic aspects of modular and Shimura varieties
14G35 Modular and Shimura varieties
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