In mathematics, Serre's modularity conjecture, introduced by Serre (1975, 1987) based on some 1973–1974 correspondence with John Tate, states that an odd irreducible two-dimensional Galois representation over a finite field arises from a modular form, and a stronger version of his conjecture specifies the weight and level of the modular form. It is proved by Chandrashekhar Khare in the level 1 case in 2005 and later in 2008 a proof of the full conjecture is worked out jointly by Chandrashekhar Khare and Jean-Pierre Wintenberger.
Read more about Serre's Modularity Conjecture: Formulation, Optimal Level and Weight, Proof
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