Related papers: On the quaternionic Serre weights
We study the possible weights of an irreducible two-dimensional mod p representation of the absolute Galois group of F which is modular in the sense of that it comes from an automorphic form on a definite quaternion algebra with centre F…
We prove a version of the weight part of Serre's conjecture for mod $p$ Galois representations attached to automorphic forms on rank 2 unitary groups which are non-split at $p$. More precisely, let $F/F^+$ denote a CM extension of a totally…
We formulate and prove the weight part of Serre's conjecture for three-dimensional mod $p$ Galois representations under a genericity condition when the field is unramified at $p$. This removes the assumption in \cite{arXiv:1512.06380},…
We show that the modular Serre weights of a sufficiently generic mod $p$ Galois representation of an unramified $p$-adic field are themselves generic, and give precise bounds on the genericity, by extending previous work of Emerton, Gee and…
We study the weight part of Serre's conjecture for generic $n$-dimensional mod $p$ Galois representations. We first generalize Herzig's conjecture to the case where the field is ramified at $p$ and prove the weight elimination direction of…
Under some technical assumptions of a global nature, we establish the weight part of Serre's conjecture for mod $p$ Galois representations for CM fields that are tamely ramified and sufficiently generic at $p$.
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,…
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…
A two-dimensional Galois representation into the Hecke algebra of Katz modular forms of weight one over a finite field of characteristic p is constructed and is shown to be unramified at p in most cases.
We prove the `weight elimination' part of the weight part of Serre's conjecture for mod 2 Galois representations for rank two unitary groups, by modifying the results in arXiv:1203.2552 and arXiv:1309.0527.
We present a Serre-type conjecture on the modularity of four-dimensional symplectic mod p Galois representations. We assume that the Galois representation is irreducible and odd (in the symplectic sense). The modularity condition is…
We study the possible weights of an irreducible 2-dimensional modular mod p representation of the absolute Galois group of F, where F is a totally real field which is totally ramified at p, and the representation is tamely ramified at the…
We determine reductions of 2-dimensional, irreducible, semi-stable, and non-crystalline representations of $\mathrm{Gal}(\overline{\mathbb Q}_p/\mathbb Q_p)$ with Hodge--Tate weights $0 < k-1$ and with $\mathcal L$-invariant whose $p$-adic…
We prove the level 1 case of Serre's conjecture.
We study the weight part of (a generalisation of) Serre's conjecture for mod l Galois representations associated to automorphic representations on unitary groups of rank n for odd primes l. Given a modular Galois representation, we use…
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 construct moduli stacks of two-dimensional mod p representations of the absolute Galois group of a p-adic local field, and relate their geometry to the weight part of Serre's conjecture for GL(2).
We consider mod $p$ Hilbert modular forms for a totally real field $F$, viewed as sections of automorphic line bundles on Hilbert modular varieties in prime characteristic $p$. For a Hecke eigenform of arbitrary weight, we prove the…
We formulate a Serre-type conjecture for n-dimensional Galois representations that are tamely ramified at p. The weights are predicted using a representation-theoretic recipe. For n = 3 some of these weights were not predicted by the…
We prove the weight part of Serre's conjecture for Galois representations valued in $\mathrm{GSp}_4$ that are tamely ramified with explicit genericity at places above $p$ as conjectured by Herzig--Tilouine and Gee--Herzig--Savitt. This…