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Reduction modulo $ p$ of certain semi-stable representations


Author: Chol Park
Journal: Trans. Amer. Math. Soc. 369 (2017), 5425-5466
MSC (2010): Primary 11F80
DOI: https://doi.org/10.1090/tran/6827
Published electronically: February 13, 2017
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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.


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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

DOI: https://doi.org/10.1090/tran/6827
Received by editor(s): July 20, 2014
Received by editor(s) in revised form: August 27, 2015
Published electronically: February 13, 2017
Article copyright: © Copyright 2017 American Mathematical Society