Explicit Serre weights for two-dimensional Galois representations

Abstract

We prove the explicit version of the Buzzard–Diamond–Jarvis conjecture formulated by Dembeleet al.(Serre weights and wild ramification in two-dimensional Galois representations, Preprint (2016),arXiv:1603.07708[math.NT]). More precisely, we prove that it is equivalent to the original Buzzard–Diamond–Jarvis conjecture, which was proved for odd primes (under a mild Taylor–Wiles hypothesis) in earlier work of the third author and coauthors.