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COMPACTIFICATIONS OF SUBSCHEMES OF INTEGRAL MODELS OF SHIMURA VARIETIES

Part of: Discontinuous groups and automorphic forms Arithmetic algebraic geometry

Published online by Cambridge University Press:  24 September 2018

KAI-WEN LAN  and
BENOÎT STROH
KAI-WEN LAN
Affiliation:
University of Minnesota, Minneapolis, MN 55455, USA; kwlan@math.umn.edu
BENOÎT STROH
Affiliation:
C.N.R.S. and Institut de Mathématiques de Jussieu–Paris Rive Gauche, 75252 Paris Cedex 05, France; benoit.stroh@imj-prg.fr

Abstract

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We study several kinds of subschemes of mixed characteristic models of Shimura varieties which admit good (partial) toroidal and minimal compactifications, with familiar boundary stratifications and formal local structures, as if they were Shimura varieties in characteristic zero. We also generalize Koecher’s principle and the relative vanishing of subcanonical extensions for coherent sheaves, and Pink’s and Morel’s formulas for étale sheaves, to the context of such subschemes.

MSC classification

Primary: 11G18: Arithmetic aspects of modular and Shimura varieties
Secondary: 11G15: Complex multiplication and moduli of abelian varieties 11F75: Cohomology of arithmetic groups
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 6 , 2018 , e18
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits noncommercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s) 2018

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