2006/03/17 by Luís Dieulefait, Dieulefait, Luis · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.math/0603439
openalex publication_date 2006/03/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 at all characteristic 2 representations at any step of our proof). The key tool in the proof is a very general modularity lifting result of Kisin, which is combined with the methods and results of previous articles on Serre's conjecture by Khare, Wintenberger, and the author, and modularity results of Schoof for semistable abelian varieties of small conductor. Assuming GRH, infinitely many cases of even level will also be proved.