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Mathematics > Algebraic Geometry

arXiv:1403.3962 (math)
[Submitted on 16 Mar 2014]

Title:The congruence relation in the non-PEL case

Authors:Oliver Bueltel
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Abstract:This work settles the Eichler-Shimura congruence relation of Blasius and Rogawski for certain 5-dimensional Hodge-type Shimura varieties, that were not tractable by previously known methods. In a more general context we introduce a hypothesis called (NVC) on the behavior of Hecke correspondences, and show that it implies the congruence relation. A major ingredient in the proof of this result is a theorem of this http URL on CM-lifts of ordinary points in characteristic p, along with an analysis of the mod p-reductions of various Hecke translates of that CM-lift. Finally we prove this (NVC)-hypothesis for our particular Shimura 5-folds, and in doing so we obtain an unconditional result for the congruence relation of these non-PEL examples.
Comments: This corrects a mistake in the appendix of the published version
Subjects: Algebraic Geometry (math.AG)
MSC classes: 11G18, 14G35, 11F55, 14K22
Cite as: arXiv:1403.3962 [math.AG]
  (or arXiv:1403.3962v1 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1403.3962
Journal reference: J. reine angew. Math. 544(2002) p.133-159

Submission history

From: Oliver Bültel [view email]
[v1] Sun, 16 Mar 2014 21:52:48 UTC (25 KB)
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