Related papers: On the reductions of certain two-dimensional cryst…

We prove the indecomposability of Galois representation restricted to the p-decomposition group attached to a non CM nearly p-ordinary weight two Hilbert modular form under mild conditions.

Using differential techniques, we compute the Jacquet module of the locally analytic vectors of irreducible admissible unitary representations of GL_2(\qp). This gives a direct proof of some results of Colmez, leading to a proof of…

We show that any two-dimensional odd dihedral representation \rho over a finite field of characteristic p>0 of the absolute Galois group of the rational numbers can be obtained from a Katz modular form of level N, character \epsilon and…

Multidimensional contractions of irreducible representations of Cayley--Klein orthogonal algebras in Gel'fand--Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method of…

The Galois representation associated to a p-divisible group over a complete noetherian normal local ring with perfect residue field is described in terms of its Dieudonn\'e display. As a corollary we deduce in arbitrary characteristic…

Let $p$ be an odd prime. Let $\rho: G_F \to \mathrm{GL}_2(\overline{\mathbb{F}}_p)$ be a Galois representation of a totally real field $F$. For a small partial weight one weight $(k,0)$, we prove that modularity of $\rho$ can be…

Let K be a totally real Galois number field and let A be a set of elliptic curves over K. We give sufficient conditions for the existence of a finite computable set of rational primes P such that for p not in P and E in A, the…

We give a classification of irreducible admissible modulo $p$ representations of a split $p$-adic reductive group in terms of supersingular representations. This is a generalization of a theorem of Herzig.

Let F be a totally real field, and v a place of F dividing an odd prime p. We study the weight part of Serre's conjecture for continuous, totally odd, two-dimensional mod p representations rhobar of the absolute Galois group of F that are…

We prove the Breuil-M\'ezard conjecture for 2-dimensional potentially Barsotti-Tate representations of the absolute Galois group G_K, K a finite extension of Q_p, for any p>2 (up to the question of determining precise values for the…

The global deformation theory of residually reducible Galois representations with fixed auxiliary conditions is studied. We show that $\bar{\rho}:\operatorname{Gal}(\bar{\mathbb{Q}}/\mathbb{Q})\rightarrow…

We study the crystalline universal deformation ring R (and its ideal of reducibility I) of a mod p Galois representation rho_0 of dimension n whose semisimplification is the direct sum of two absolutely irreducible mutually non-isomorphic…

In this article we consider mod p modular Galois representations which are unramified at p such that the Frobenius element at p acts through a scalar matrix. The principal result states that the multiplicity of any such representation is…

We adapt a technique of Kisin to construct and study crystalline deformation rings of $G_K$ for a finite extension $K/\mathbb{Q}_p$. This is done by considering a moduli space of Breuil--Kisin modules, satisfying an additional Galois…

Let $p\geq 5$ be a prime number. In this paper, we construct Galois representations associated with modular forms for which the dimension of the $p$-torsion in the Bloch-Kato Selmer group can be made arbitrarily large. Our result extends…

Multidimensional contractions of irreducible representations of the Cayley-Klein unitary algebras in the Gel'fand-Zetlin basis are considered. Contracted over different parameters, algebras can turn out to be isomorphic. In this case method…

Let $n \geq 2$ and $p$ be a prime. Let $K$ be a number field and consider two Galois representations $\rho_1, \rho_2 : \operatorname{Gal}(\overline{K} / K) \to \operatorname{GL}_n(\mathbb{Z}_p)$ having residual image a $p$-group. We explain…

We address the problem of the determination of the images of three-dimensional geometric and modular Galois representations. In the modular case the existence of these representations is only conjectural. We give conditions to ensure that…

Let $p$ be an odd prime and $q$ a power of $p$. We examine the deformation theory of reducible and indecomposable Galois representations $\bar{\rho}:G_{\mathbb{Q}}\rightarrow \text{GSp}_{2n}(\mathbb{F}_q)$ that are unramified outside a…

We classify irreducible unitary representations of the group of all infinite matrices over a $p$-adic field ($p\ne 2$) with integer elements equipped with a natural topology. Any irreducible representation passes through a group $GL$ of…