A note on reductions of $2$-dimensional crystalline Galois representations
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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.References
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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
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3251713