Israel Journal of Mathematics

, Volume 219, Issue 1, pp 1–70 | Cite as

Iwasawa modules and p-modular representations of GL2

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Abstract

Let F be a finite extension of Q p . We associate, to certain smooth pmodular representations π of GL 2(F), a module \(\mathfrak{S}(\pi )\) on the mod-p Iwasawa algebra of the standard Iwahori subgroup I of GL 2(F). When F is unramified, we obtain a module on a suitable formally smooth F q-algebra, endowed with an action of \(\mathcal{O}_F^ \times \) (the units in the ring of integers of F) and an \(\mathcal{O}_F^ \times \) equivariant, Frobenius semilinear endomorphism which turns out to be p-étale. We study the torsion properties of such a module, as well as its Iwahori-radical filtration.

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© Hebrew University of Jerusalem 2017

Authors and Affiliations

  1. 1.Université Montpellier 2MontpellierFrance

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