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Filtered modules corresponding to potentially semi-stable representations. (English) Zbl 1217.11112
Let \(p>2\) be a prime number, \(K\) a \(p\)-adic field, with the absolute Galois group \(G_K\). The author parametrizes two-dimensional potentially semi-stable \(p\)-adic representations of \(G_K\) with coefficients in a \(p\)-adic field \(E\) by \([K:{\mathbb Q}_p]\) elements of \({\mathbb P}^1(E)\).

MSC:
11S20 Galois theory
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[1] Breuil, C.; Mézard, A., Multiplicités modulaires et représentations de \(\mathit{GL}_2(\mathbf{Z}_p)\) et de \(\operatorname{Gal}(\overline{\mathbf{Q}}_p / \mathbf{Q}_p)\) en \(\ell = p\), Duke math. J., 115, 2, 205-310, (2002)
[2] Colmez, P.; Fontaine, J.-M., Construction des représentations p-adiques semi-stables, Invent. math., 140, 1, 1-43, (2000) · Zbl 1010.14004
[3] Dousmanis, G., Rank two filtered \((\phi, N)\)-modules with Galois descent data and coefficients, Trans. amer. math. soc., 362, 7, 3883-3910, (2010) · Zbl 1209.11050
[4] Fontaine, J.-M.; Mazur, B., Geometric Galois representations, (), 41-78 · Zbl 0839.14011
[5] Fontaine, J.-M., Le corps des périodes p-adiques, Astérisque, 223, 59-111, (1994) · Zbl 0940.14012
[6] Ghate, E.; Mézard, A., Filtered modules with coefficients, Trans. amer. math. soc., 361, 5, 2243-2261, (2009) · Zbl 1251.11044
[7] Savitt, D., On a conjecture of conrad, diamond, and Taylor, Duke math. J., 128, 1, 141-197, (2005) · Zbl 1101.11017
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