An irreducibility criterion for supersingular 𝐦𝐨𝐝 𝐩 representations of 𝐆𝐋₂(𝐅) for totally ramified extensions 𝐅 of ℚ_{𝕡}

Schein, Michael

doi:10.1090/S0002-9947-2011-05478-4

An irreducibility criterion for supersingular $\mathbf {mod}$ $p$ representations of $\operatorname {GL}_2(F)$ for totally ramified extensions $F$ of $\mathbb {Q}_p$
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Trans. Amer. Math. Soc. 363 (2011), 6269-6289 Request permission

Abstract:

Let $F$ be a totally ramified extension of $\mathbb {Q}_p$. We consider supersingular representations of $\mathrm {GL}_2(F)$ whose socles as $\mathrm {GL}_2(\mathcal {O}_F)$-modules are of a certain form that is expected to appear in the mod $p$ local Langlands correspondence and establish a condition under which they are irreducible.

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