Related papers: The level 1 weight 2 case of Serre's conjecture
We prove existence of conjugate Galois representations, and we use it to derive a simple method of weight reduction. As a consequence, an alternative proof of the level 1 case of Serre's conjecture follows.
In this appendix, we observe that our March preprint on Serre's conjecture was indeed correct: the only "missing argument" follows automatically from a result of Bockle and Ramakrishna. Thus, we get a proof of the level 1 weight 2 case of…
In this article we give a proof of Serre's conjecture for the case of odd level and arbitrary weight. Our proof does not depend on any generalization of Kisin's modularity lifting results to characteristic 2 (moreover, we will not consider…
The purpose of this short note is to present a simplified proof of Serre's modularity conjecture using the strong modularity lifting results currently available. This second version includes extra details on definitions and proofs than the…
We prove the level 1 case of Serre's conjecture.
A particular case of the level increasing conjecture for type A fusion coefficientes is proved for when one the weights is a multiple of the first fundamental weight.
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 formulate a number of related generalisations of the weight part of Serre's conjecture to the case of GL(n) over an arbitrary number field, motivated by the formalism of the Breuil-M\'ezard conjecture. We give evidence for these…
We provide new sufficient conditions under which Ryser's conjecture holds.
The Serre conjecture II predicts that every torsor under a semisimple, simply connected, algebraic group over a field of cohomological dimension at most 2 and of degree of imperfection at most 1 has a rational point. We generalize this…
In this paper, we prove a conjecture of Schnell in the surface case.
Let p>2 be prime. We complete the proof of the weight part of Serre's conjecture for rank two unitary groups for mod p representations in the totally ramified case, by proving that any weight which occurs is a predicted weight. Our methods…
We prove the Aharoni Berger Conjecture
In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.
This brief note only contains a modest contribution: we just fix some inaccuracies in the proof of the prime level weight 2 case of Serre's conjecture given in Khare's preprint "On Serre's modularity conjecture for 2-dimensional mod 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,…
We provide a proof of a variant of the Landau-Siegel Zeros conjecture.
New cases of the multiplicity conjecture are considered.
We provide a short proof of the 1-dimensional flat chain conjecture.
We show that a weak form of the generalized Bocherer's conjecture implies multiplicity one for Siegel cusp forms of degree 2.