Back Serre-Vermutung German Conjetura de modularidad de Serre Spanish Conjecture de modularité de Serre French Serres modularitetsförmodan Swedish
| Field | Algebraic number theory |
|---|---|
| Conjectured by | Jean-Pierre Serre |
| Conjectured in | 1975 |
| First proof by | Chandrashekhar Khare Jean-Pierre Wintenberger |
| First proof in | 2008 |
In mathematics, Serre's modularity conjecture, introduced by Jean-Pierre Serre (1975, 1987), states that an odd, irreducible, two-dimensional Galois representation over a finite field arises from a modular form. A stronger version of this conjecture specifies the weight and level of the modular form. The conjecture in the level 1 case was proved by Chandrashekhar Khare in 2005,[1] and a proof of the full conjecture was completed jointly by Khare and Jean-Pierre Wintenberger in 2008.[2]
- ^ Khare, Chandrashekhar (2006), "Serre's modularity conjecture: The level one case", Duke Mathematical Journal, 134 (3): 557–589, doi:10.1215/S0012-7094-06-13434-8.
- ^ Khare, Chandrashekhar; Wintenberger, Jean-Pierre (2009), "Serre's modularity conjecture (I)", Inventiones Mathematicae, 178 (3): 485–504, Bibcode:2009InMat.178..485K, CiteSeerX 10.1.1.518.4611, doi:10.1007/s00222-009-0205-7 and Khare, Chandrashekhar; Wintenberger, Jean-Pierre (2009), "Serre's modularity conjecture (II)", Inventiones Mathematicae, 178 (3): 505–586, Bibcode:2009InMat.178..505K, CiteSeerX 10.1.1.228.8022, doi:10.1007/s00222-009-0206-6.
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