Related papers: Irregular loci in the Emerton-Gee stack for GL_2

We prove that the irreducible components of the space of framed deformations of the trivial 2-dimensional mod 2 representation of the absolute Galois group of Q_2 are in natural bijection with those of the trivial character, confirming a…

The aim of this paper is to extend some arithmetic results on elliptic modular forms to the case of Hilbert modular forms. Among these results let's mention : (1) the control of the image of the Galois representation modulo $p$, (2) Hida's…

We extend Colmez's functor defined for $\operatorname{GL}_2(\mathbf{Q}_p)$ to the category of finitely generated smooth admissible mod-$p$ representations of the two-fold metaplectic cover of $\operatorname{GL}_2(\mathbf{Q}_p)$. We compute…

Let $p$ be an odd prime, and $\mathbf{Q}_{p^f}$ the unramified extension of $\mathbf{Q}_p$ of degree $f$. In this paper, we reduce the problem of constructing strongly divisible modules for $2$-dimensional semi-stable non-crystalline…

Let K_0 be a finite unramified extension of Q_p. We show that all crystalline representations of G_{K_0} (the absolute Galois group of K_0) with Hodge-Tate weights in {0, ..., p-1} are potentially diagonalizable.

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…

The main result of this article states that the Galois representation attached to a Hilbert modular eigenform defined over F_p^bar of parallel weight 1 and level prime to p is unramified above p. This includes the important case of…

We show for all local fields $K/\mathbb{Q}_p$, with $p >3$, all representations $\bar\rho:G_K \to G_2(\bar{\mathbb{F}}_p)$ admit a crystalline lift $\rho: G_K\to G_2(\bar{\mathbb{Z}}_p)$, where $G_2$ is the exceptional Chevalley group of…

Let $p$ be a prime number and $r$ a non-negative integer. In this paper, we prove that there exists an anti-equivalence between the category of weak $(\varphi,\hat{G})$-modules of height $r$ and a certain subcategory of the category of…

Let $p$ be a prime number, $F$ a totally real number field unramified at places above $p$ and $D$ a quaternion algebra of center $F$ split at places above $p$ and at no more than one infinite place. Let $v$ be a fixed place of $F$ above $p$…

We establish a geometrisation of the Breuil-M\'ezard conjecture for potentially Barsotti-Tate representations, as well as of the weight part of Serre's conjecture, for moduli stacks of two-dimensional mod p representations of the absolute…

Given a totally real number field $F$ and a mod $p$ Galois representation $\rho\colon G_F\to \mathrm{GL}_2(\bar{\mathbf{F}}_p)$, we propose an explicit definition of the set of Serre weights $W(\rho)$ attached to $\rho$. We prove that our…

Let $p>2$ be prime, and let $F$ be a totally real field in which $p$ is unramified. We give a sufficient criterion for a mod $p$ Galois representation to arise from a mod $p$ Hilbert modular form of parallel weight one, by proving a…

The conjecture of Serre referred in the title is the one about modularity of odd Galois representations into GL(2,F) where F is a finite field of characteristic p. We present an analogous conjecture where GL(2) is replaced by GL(n). We…

We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on rank two unitary groups for odd primes l. We propose a conjectural set of Serre weights,…

We prove modularity of certain residually reducible ordinary 2-dimensional $p$-adic Galois representations with determinant a finite order odd character $\chi$. For certain non-quadratic $\chi$ we prove an $R=T$ result for $T$ the weight 1…

Let F be a totally real field and p an odd prime. If r is a continuous, semisimple, totally odd mod p representation of the absolute Galois group of F which is tamely ramified at all places of F dividing p, then we formulate a conjecture…

Let $F$ be a totally real number field and let $p$ be a prime unramified in $F$. We prove the existence of Galois pseudo-representations attached to mod $p^m$ Hecke eigenclasses of paritious weight occurring in the coherent cohomology of…

For a quadratic field K, we investigate continuous mod p representations of the absolute Galois groups of K that are unramified away from p and infinity. We prove that for certain pairs (K,p), there are no such irreducible representations.…

A generalization of Serre's Conjecture asserts that if $F$ is a totally real field, then certain characteristic $p$ representations of Galois groups over $F$ arise from Hilbert modular forms. Moreover it predicts the set of weights of such…