We prove new cases of the Fontaine-Mazur conjecture, that a $2 $-dimensional $ p $-adic
representation $\rho $ of $ G_ {\mathbb {Q}, S} $ which is potentially semi-stable at $ p …

Colmez, Pierre. Représentations triangulines de dimension $2 $, dans Représentations $ p
$-adiques de groupes $ p $-adiques I: représentations galoisiennes et $(\varphi,\Gamma) …

The p-adic local Langlands correspondence for GL_2 (Q_p) is given by an exact functor
from unitary Banach representations of GL_2 (Q_p) to representations of the absolute Galois …

The slope filtration theorem gives a partial analogue of the eigenspace decomposition of a
linear transformation, for a Frobenius-semilinear endomorphism of a finite free module over …

The emerging p-adic Langlands programme Page 1 Proceedings of the International Congress
of Mathematicians Hyderabad, India, 2010 The emerging p-adic Langlands programme …

On the Breuil-Mézard conjecture Page 1 ON THE BREUIL–MÉZARD CONJECTURE
VYTAUTAS PAŠK UNAS Abstract We give a new local proof of the Breuil–Mézard conjecture …

We show that the Euler system associated with Rankin–Selberg convolutions of modular
forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular …

We develop a theory of Selmer groups for analytic families of Galois representations, which
are only assumed “ordinary” on the level of their underlying (φ, Γ)-modules. Our approach …

The theory of (φ q, Γ)-modules is a generalization of Fontaine's theory of (φ, Γ)-modules,
which classifies G F-representations on O F-modules and F-vector spaces for any finite …

Nous décrivons le complexe de de Rham des revĉtements du demi-plan de Drinfeld pour
$\mathrm {GL} _2 (\mathbf {Q} _p) $. Cette description, conjecturée par Breuil et Strauch …