# Deformation rings and parabolic induction

17 Oct 2017 Hauseux Julien Schmidt Tobias Sorensen Claus

We study deformations of smooth mod $p$ representations (and their duals) of a $p$-adic reductive group $G$. Under some mild genericity condition, we prove that parabolic induction with respect to a parabolic subgroup $P=LN$ defines an isomorphism between the universal deformation rings of a supersingular representation $\bar{\sigma}$ of $L$ and of its parabolic induction $\bar{\pi}$... (read more)

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• REPRESENTATION THEORY
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