Related papers: Serre weights for quaternion algebras

Let K_{f} be the finite unramified extension of Q_{p} of degree f and E any finite large enough coefficient field containing K_{f}. We construct analytic families of \'etale (Phi,Gamma)-modules which give rise to families of crystalline…

We prove an integral R = T theorem for odd two dimensional p-adic representations of the absolute Galois group which are unramified at p, extending results of [CG] to the non-minimal case. We prove, for any p, the existence of Katz modular…

Motives and automorphic forms of arithmetic type give rise to Galois representations that occur in {\it compatible families}. These compatible families are of p-adic representations with p varying. By reducing such a family mod p one…

We investigate the representation theory of a large class of pointed Hopf algebras, extending results of Lusztig and others. We classify all simple modules in a suitable category and determine the weight multiplicities; we establish a…

In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\mathrm{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_{\ell})$, with $F$ a totally real number field and $G$ a reductive group, to…

Using $p$-adic local Langlands correspondence for $\operatorname{GL}_2(\mathbb{Q}_2)$ and an ordinary $R = \mathbb{T}$ theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the…

Let K be a finite extension of Qp. We fix a continuous absolutely irreducible representation of the absolute Galois group of K over a finite dimensional vector space with coefficient in a finite field of characteristic p and consider its…

Irreducible nonzero level modules with finite-dimensional weight spaces are studied for non-twisted affine Lie superalgebras. A complete classification is obtained for superalgebras A(m,n)^ and C(n)^. In other cases the classification…

We consider lifting of mod p representations to mod p^2 representations in the setting of representations of (i) finite groups; (ii) absolute Galois groups of abstract fields; and (iii) absolute Galois groups of local and global fields.

In this note we prove the non existence of certain irreducible two dimensional representations of the the absolute Galois group. Such results are predicted by Serre's conjecture and we use Fontaine's methods to verify these predictions in a…

Serre's strong conjecture, now a theorem of Khare and Wintenberger, states that every two-dimensional continuous, odd, irreducible mod $p$ Galois representation $\rho$ arises from a modular form of a specific minimal weight $k(\rho)$, level…

We show that the completed Hecke algebra of $p$-adic modular forms is isomorphic to the completed Hecke algebra of continuous $p$-adic automorphic forms for the units of the quaternion algebra ramified at $p$ and $\infty$. This gives an…

We construct and study the moduli of continuous representations of a profinite group with integral $p$-adic coefficients. We present this moduli space over the moduli space of continuous pseudorepresentations and show that this morphism is…

We establish the automorphy of some families of 2-dimensional representations of the absolute Galois group of a totally real field, which do not satisfy the so-called `Taylor--Wiles hypothesis'. We apply this to the problem of the…

We give a method of constructing polynomials of arbitrarily large degree irreducible over a global field F but reducible modulo every prime of F. The method consists of finding quadratic f in F[x] whose iterates have the desired property,…

Suppose that $G$ is a simple adjoint reductive group over $\mathbf{Q}$, with an exceptional Dynkin type, and with $G(\mathbf{R})$ quaternionic (in the sense of Gross-Wallach). Then there is a notion of modular forms for $G$, anchored on the…

Let F be a local field with finite residue field of characteristic p, D the quaternion division algebra with centre F, and R an algebraically closed field of any characteristic. We classify the smooth irreducible R-representations V of the…

Let p > 2 be prime. We prove the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the unramified case (that is, the Buzzard-Diamond-Jarvis conjecture for unitary groups), by proving that any Serre…

We study finite-dimensional representations of hyper loop algebras over non-algebraically closed fields. The main results concern the classification of the irreducible representations, the construction of the Weyl modules, base change,…

Let $F$ be a totally real field of even degree in which $p$ splits completely. Let $\overline{r}:G_F \rightarrow \mathrm{GSp}_4(\overline{\mathbb{F}}_p)$ be a modular Galois representation unramified at all finite places away from $p$ and…