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Gee, Toby; Kisin, Mark
The Breuil-Mézard conjecture for potentially Barsotti-Tate representations. (English) Zbl 1408.11033
Forum Math. Pi 2, Paper No. e1, 56 p. (2014).
Summary: We prove the Breuil-Mézard conjecture for two-dimensional potentially Barsotti-Tate representations of the absolute Galois group \(G_{K}\), \(K\) a finite extension of \(\mathbb{Q}_{p}\), for any \(p>2\) (up to the question of determining precise values for the multiplicities that occur). In the case that \(K/\mathbb{Q}_{p}\) is unramified, we also determine most of the multiplicities. We then apply these results to the weight part of Serre’s conjecture, proving a variety of results including the Buzzard-Diamond-Jarvis conjecture.

Cited in 30 Documents
MSC:
11F33 Congruences for modular and \(p\)-adic modular forms
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\textit{T. Gee} and \textit{M. Kisin}, Forum Math. Pi 2, Paper No. e1, 56 p. (2014; Zbl 1408.11033)
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