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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

An irreducibility criterion for supersingular $ \mathbf{mod}$ $ p$ representations of $ \operatorname{GL}_2(F)$ for totally ramified extensions $ F$ of $ \mathbb{Q}_p$


Author: Michael M. Schein
Journal: Trans. Amer. Math. Soc. 363 (2011), 6269-6289
MSC (2010): Primary 11S37, 11F80
Published electronically: June 27, 2011
MathSciNet review: 2833554
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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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Additional Information

Michael M. Schein
Affiliation: Department of Mathematics, Bar Ilan University, Ramat Gan 52900, Israel
Email: mschein@math.biu.ac.il

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05478-4
PII: S 0002-9947(2011)05478-4
Keywords: Supersingular representations, mod $p$ local Langlands correspondence, Galois representations
Received by editor(s): August 14, 2009
Received by editor(s) in revised form: September 24, 2009
Published electronically: June 27, 2011
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.