The congruence relation in the non-PEL case
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 R.Noot 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.
Cite
@article{arxiv.1403.3962,
title = {The congruence relation in the non-PEL case},
author = {Oliver Bueltel},
journal= {arXiv preprint arXiv:1403.3962},
year = {2014}
}
Comments
This corrects a mistake in the appendix of the published version