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On reduction of Hilbert-Blumenthal varieties

Chia-Fu Yu — 2003

Annales de l'Institut Fourier

Let O 𝐅 be the ring of integers of a totally real field 𝐅 of degree g . We study the reduction of the moduli space of separably polarized abelian O 𝐅 -varieties of dimension g modulo p for a fixed prime p . The invariants and related conditions for the objects in the moduli space are discussed. We construct a scheme-theoretic stratification by a -types on the Rapoport locus and study the relation with the slope stratification. In particular, we recover the main results of Goren and Oort [J. Alg. Geom.,...

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