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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Morra, S. Iwasawa modules and p-modular representations of GL2. Isr. J. Math. 219, 1–70 (2017). https://doi.org/10.1007/s11856-017-1473-3
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DOI: https://doi.org/10.1007/s11856-017-1473-3