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on the hilbert–blumenthal moduli problem

Published online by Cambridge University Press:  29 July 2005

inken vollaard
inken vollaard
Affiliation:
mathematisches institut, universität bonn, beringstraβe 1, 53115 bonn, germany (vollaard@math.uni-bonn.de)
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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 $\mathrm{spec}\mathbb{z}_{(p)}$. we also examine the associated local models and prove that they are equal.

Keywords

hilbert–blumenthal varietiesbad reduction of shimura varietiesabelian schemes with real multiplicationlocal modelsprimary 14g3511g1814k10secondary 14k1511g10
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 4 , Issue 4 , October 2005 , pp. 653 - 683
Copyright
2005 cambridge university press

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