# zbMATH — the first resource for mathematics

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
Full Text:
##### References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.