Explicit Serre weights for two-dimensional Galois representations

Abstract

We prove the explicit version of the Buzzard-Diamond-Jarvis conjecture formulated by Dembele et 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.