Reduction modulo 𝑝 of certain semi-stable representations

Park, Chol

doi:10.1090/tran/6827

Reduction modulo $p$ of certain semi-stable representations
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by Chol Park PDF

Trans. Amer. Math. Soc. 369 (2017), 5425-5466 Request permission

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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