… In this section we will recall the formalism of the general Breuil–Mézard conjecture for GLn,
following [EG14], and then explain how the formalism leads to a Serre weight conjecture. As …

… Later, for another reason ( 27]), Serre … weight 1 without problem. As a consequence we have
to change the de nition of k if we want the conjecture to specify the minimal possible weight k…

… with the Serre weight conjectures of [5], which can be viewed as specifying the weights .k;l/
2 Z† … Our method is indicative of a general strategy for transferring results from the setting of …

… a conjecture generalising the weight in Serre’s Conjecture to … A weight in this context is an
irreducible representation of G … The conjecture describes the predicted set of weights in terms …

… Serre (finite field representations). We focus mainly on this conjecture of Serre thereafter that
we call Serre’… Weights greater than two: In general motives over Q of rank two that are odd (…

… ) Serre weights at v. Buzzard, Diamond, and Jarvis in [BDJ] formulated a Serre-type conjecture
for … We would like to have a conjecture in the general case. We may assume that F = Q, as …

… , because in general the connection between being modular of some Serre weight and having
… We define a global notion of Serre weight by taking a product of local Serre weights in the …

… It is this correspondence, conjectured by Langlands, which we establish here. The first three
sections are preliminary. The fourth section contains the statement of the main theorem and …

… today about Serre's conjecture, we will discuss the differences between Conjecture 1.8 and
[37… For a detailed proof of in fact more general results we refer to [32, §6-§8]; our aim is just to …

… We study the weight part of (a generalisation of) Serre’s conjecture for mod l Galois
representations … This is one of the motivations for the general Serre weight conjectures explained …