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Sur quelques représentations potentiellement cristallines de GL_2(Q_p)  [PDF]
L. Berger,C. Breuil
Mathematics , 2006,
Abstract: To each 2-dimensional irreducible p-adic representation of Gal(Qpbar/Qp) which becomes crystalline over an abelian extension of Q_p, we associate a Banach space B(V) endowed with a linear continuous unitary action of GL_2(Q_p). When V is moreover phi-semi-simple, we use the (phi,Gamma)-module and the Wach module associated to V to show that the representation B(V) is nonzero, topologically irreducible and admissible.
Hochschild cohomology of $GL_2(\bar{\mathbb{F}}_p)$  [PDF]
Vanessa Miemietz,Will Turner
Mathematics , 2011,
Abstract: We compute the Hochschild cohomology algebra of $GL_2$ over an algebraically closed field of characteristic $p>2$.
The Weyl extension algebra of $GL_2(\bar{\mathbb{F}}_p)$  [PDF]
Vanessa Miemietz,Will Turner
Mathematics , 2011,
Abstract: We compute the Yoneda extension algebra of the collection of Weyl modules for $GL_2$ over an algebraically closed field of positive characteristic p by developing a theory of generalised Koszul duality for certain 2-functors, one of which controls the rational representation theory of $GL_2$ over such a field.
Sur certains complétés unitaires universels explicites pour GL_2(F)  [PDF]
Marco De Ieso
Mathematics , 2011,
Abstract: In this paper we give an explicit description of the universal unitary completion of certain locally Q_p-analytic representations of GL_2(F), where F is a finite extension of Q_p (this generalizes some results of Berger-Breuil for F=Q_p). To this aim, we make use of certain Banach spaces of C^r functions on O_F (for r a positive real number) introduced by the author.
Sur la fidélité de certaines représentations de GL_2(F) sous une algèbre d'Iwasawa  [PDF]
Hu Yongquan,Morra Stéfano,Schraen Benjamin
Mathematics , 2011,
Abstract: Let F be a finite extension of Qp, O_F its ring of integers and E a finite extension of Fp. The natural action of the unit group O_F* on O_F extends in a continuous action on the Iwasawa algebra E[[O_F]]. In this work, we show that non zero ideals of E[[O_F]] which are stable under O_F* are open. As a consequence, we deduce the fidelity of the action of E[[U]], with U the subgroup of upper unipotent matrices in GL2(O_F) on an irreducible admissible smooth E-representation of GL2(F). ----- Soit F une extension finie de Qp, d'anneau des entiers O_F et E une extension finie de Fp. L'action naturelle du groupes des unit\'es O_F* sur O_F se prolonge alors en une action continue sur l'alg\`ebre d'Iwasawa E[[O_F]]. Dans ce travail, on d\'emontre que les id\'eaux non nuls de E[[O_F]] stables par O_F* sont ouverts. En particulier, on en d\'eduit la fid\'elit\'e de l'action de l'alg\`ebre d'Iwasawa des matrices unipotentes sup\'erieures de GL2(O_F) sur une repr\'esentation lisse irr\'eductible admissible de GL2(F).
Sur quelques descriptions antiques de la péninsule italienne  [PDF]
Mappemonde , 1986,
Abstract: Les représentations de la péninsule italienne et leurs métamorphoses dans les écrits géographiques de Polybe, Strabon et Pline l'Ancien.
Diagrammes canoniques et representations modulo $p$ de $\GL_2(F)$  [PDF]
Yongquan Hu
Mathematics , 2009,
Abstract: Let $p$ be a prime number and $F$ a local field with residual characteristic $p$. In this article, to an irreducible smooth representation of $GL_2(F)$ over $\bar{\mathbf{F}}_p$ with central character, we associate canonically a diagram which determines the original representation up to isomorphism. We also determine it in some cases.
Admissible unitary completions of locally $Q_p$-rational representations of $GL_2(F)$  [PDF]
Vytautas Paskunas
Mathematics , 2008,
Abstract: Let $F$ be a finite extension of $Q_p$, $p>2$. We construct admissible unitary completions of certain representations of $GL_2(F)$ on $L$-vector spaces, where $L$ is a finite extension of $F$. When $F=Q_p$ using the results of Berger, Breuil and Colmez we obtain some results about lifting 2-dimensional mod $p$ representations of the absolute Galois group of $Q_p$ to crystabelline representations with given Hodge-Tate weights.
Category O for Rational Cherednik Algebras H_{t,c}(GL_2(F_p),h) in Characteristic p  [PDF]
Martina Balagovic,Harrison Chen
Mathematics , 2011,
Abstract: In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL_2(F_p) over an algebraically closed field of positive characteristic p, for any value of the parameter t and generic value of the parameter c.
La correspondance de Langlands locale p-adique pour GL_2(Q_p)  [PDF]
Laurent Berger
Mathematics , 2010,
Abstract: La correspondance de Langlands locale p-adique pour GL_2(Q_p) est une bijection entre certaines representations de dimension 2 de Gal(Q_p^bar/Q_p) et certaines representations de GL_2(Q_p). Cette bijection peut en fait etre construite en utilisant la theorie des (phi,Gamma)-modules et des resultats d'analyse p-adique. On deduit alors des proprietes de cette construction quelques applications interessantes en arithmetique.
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