Serre's modularity conjecture
Conjecture in number theory / From Wikipedia, the free encyclopedia
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Not to be confused with Modularity theorem.
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]
Quick Facts Field, Conjectured by ...
Field | Algebraic number theory |
---|---|
Conjectured by | Jean-Pierre Serre |
Conjectured in | 1975 |
First proof by | Chandrashekhar Khare Jean-Pierre Wintenberger |
First proof in | 2008 |
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