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Quelques conséquences des travaux d'Arthur pour le spectre et la topologie des variétés hyperboliques

En nous basant sur les résultats d'Arthur annoncés dans \cite[§30]{Arthur} nous démontrons les conjectures énoncées dans \cite{IMRN,BC,SMF} dans le cas des groupes orthogonaux à l'exclusion des groupes de type ${}^6 - D_4$. En ce qui concerne ces derniers, nous annonçons la démonstration -- encore en préparation - que leur réseaux de congruences ont toujours un $H^1$ trivial. Les démonstrations d'Arthur devraient para\^ıtre prochainement.

preprint2010arXivOpen access
Nicolas BergeronLaurent Clozel
math.GTmath.NT
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Nicolas BergeronLaurent Clozel

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