On reduction of Hilbert-Blumenthal varieties

2002/09/11 by Chia‐Fu Yu, Chia-Fu Yu, Yu, Chia-Fu
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0209114

A shortened revised version

openalex publication_date 2002/09/11 · arxiv created 2003/07/28 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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-numbers on the Rapoport locus and study the relation with the slope stratification. In particular, we recover the main results of Goren and Oort [GO, J. Alg. Geom. 2000] on the stratifications when p is unramified in O_F. We also prove the strong Grothendieck conjecture for the moduli space in some restricted cases, particularly when p is totally ramified in O_F.

Related

• Integral points on coarse Hilbert moduli schemes
• Ekedahl-Oort strata and Kottwitz-Rapoport strata
• Oort's conjecture for A_g
• Cycles on the Moduli Space of Abelian Varieties
• Compactifications of smooth families and of moduli spaces of polarized manifolds