ABOUT GALOIS REDUCIBILITY OF TORSION COHOMOLOGY CLASSES FOR KHT SHIMURA VARIETIES
Résumé
In a previous paper, we proved that the $\overline{\mathbb Z}m_l$-cohomology of KHT Shimura
varieties of dimension $d$ which is not prime, whatever is the weight of
the coefficients, when the level is large enough at $l$, always contains non trivial torsion classes.
In this work we are interested in the Galois action
on the torsion submodules in the cohomology groups of KHT Shimura varieties and we prove, at
least when $d$ is prime and $l>2d-3$ is such that the minimal prime dividing $l-1$ is $>d$,
then all Galois irreducible subquotients are of dimension
strictly less than $d$.
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