Serre's modularity conjecture

Serre's modularity conjecture
FieldAlgebraic number theory
Conjectured byJean-Pierre Serre
Conjectured in1975
First proof byChandrashekhar Khare
Jean-Pierre Wintenberger
First proof in2008

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, and a proof of the full conjecture was completed jointly by Khare and Jean-Pierre Wintenberger in 2008.

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