Reduction modulo $p$ of certain semi-stable representations
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Abstract:
Let $p>3$ be a prime number and let $G_{\mathbb {Q}_{p}}$ be the absolute Galois group of $\mathbb {Q}_{p}$. In this paper, we find Galois stable lattices in the $3$-dimensional irreducible semi-stable non-crystalline representations of $G_{\mathbb {Q}_{p}}$ with Hodge–Tate weights $(0,1,2)$ by constructing the corresponding strongly divisible modules. We also compute the Breuil modules corresponding to the mod $p$ reductions of these strongly divisible modules and determine which of the original representations has an absolutely irreducible mod $p$ reduction.References
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Additional Information
- Chol Park
- Affiliation: Korea Institute for Advanced Study, 85 Hoegiro Dondaemun-gu, Seoul 02455, Republic of Korea
- Email: cpark@kias.re.kr
- Received by editor(s): July 20, 2014
- Received by editor(s) in revised form: August 27, 2015
- Published electronically: February 13, 2017
- © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 369 (2017), 5425-5466
- MSC (2010): Primary 11F80
- DOI: https://doi.org/10.1090/tran/6827
- MathSciNet review: 3646767