A simplified proof of Serre’s conjecture

Author:

Dieulefait Luis VictorORCID,Pacetti Ariel Martín

Abstract

AbstractThe purpose of the present article is to present a simplified proof of Serre’s modularity conjecture using the strong modularity lifting results currently available.

Funder

Fundação para a Ciência e a Tecnologia

Ministerio de Ciencia, Innovación y Universidades

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Geometry and Topology,Algebra and Number Theory,Analysis

Reference41 articles.

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2. Berger, L., Li, H., Zhu, H.J.: Construction of some families of 2-dimensional crystalline representations. Math. Ann. 329(2), 365–377 (2004)

3. Deligne, P.: Formes modulaires et représentations $$l$$-adiques. In: Séminaire Bourbaki. Vol. 1968/69: Exposés 347–363, volume 175 of Lecture Notes in Math., pages Exp. No. 355, 139–172. Springer, Berlin, (1971)

4. Dieulefait, L.V.: Existence of families of Galois representations and new cases of the Fontaine-Mazur conjecture. J. Reine Angew. Math. 577, 147–151 (2004)

5. Dieulefait, L.: The level 1 weight 2 case of Serre’s conjecture. Rev. Mat. Iberoam. 23(3), 1115–1124 (2007)

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