On the Hilbert-Blumenthal moduli problem

2003/07/24 by Inken Vollaard, Vollaard, Inken
Mathematics · #11G10) #11G18 #14G35 #14K10 (14K15 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:11G18 #msc:14G35 #msc:14K10

paper · pdf · doi:10.48550/arxiv.math/0307325

33 pages, LaTeX, some typos corrected, to appear in Journal of the Inst. of Math. Jussieu, Cambridge University Press

arxiv created 2005/07/13 · arxiv updated 2009/12/01

Abstract

In this article we compare different conditions on abelian schemes with real multiplication which occur in the integral models of the Hilbert-Blumenthal Shimura variety considered by Rapoport, Deligne, Pappas and Kottwitz. We show that the models studied by Deligne/Pappas and Kottwitz are isomorphic over Spec Z_(p). We also examine the associated local models and prove that they are equal.

Related

• Integral points on Hilbert moduli schemes
• Integral points on coarse Hilbert moduli schemes
• Unitary Shimura varieties at ramified primes and arithmetic transfer
• Canonical Integral Models of Shimura Varieties of Abelian Type
• The canonicity of the integral models of RSZ Shimura varieties