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A note on reductions of $ 2$-dimensional crystalline Galois representations


Author: Gerasimos Dousmanis
Journal: Proc. Amer. Math. Soc. 142 (2014), 3713-3729
MSC (2010): Primary 11F80, 11F85
DOI: https://doi.org/10.1090/S0002-9939-2014-12163-0
Published electronically: July 17, 2014
MathSciNet review: 3251713
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Abstract: Let $ p$ be an odd prime number, $ K_{f}$ the finite unramified extension of $ \mathbb{Q} _{p}$ of degree $ f$ and $ G_{K_{f}}$ its absolute Galois group. We construct analytic families of étale $ \left ( \varphi ,\Gamma _{K_{f}}\right ) $-modules which give rise to some families of $ 2$-dimensional crystalline representations of $ G_{K_{f}}$ with length of filtration $ \geq p.$ As an application we prove that the modulo $ p$ reductions of the members of each such family (with respect to appropriately chosen Galois-stable lattices) are constant.


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Additional Information

Gerasimos Dousmanis
Affiliation: Fields Institute for Mathematics, 222 College Street, Toronto, Ontario, M5T 3J1 Canada
Address at time of publication: Athens, Greece
Email: makis.dousmanis@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-12163-0
Received by editor(s): April 18, 2012
Received by editor(s) in revised form: December 3, 2012
Published electronically: July 17, 2014
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2014 American Mathematical Society