Abstract:We prove the Breuil-Mézard conjecture for 2-dimensional potentially Barsotti-Tate representations of the absolute Galois group G_K, K a finite extension of Q_p, for any p>2 (up to the question of determining precise values for the multiplicities that occur). In the case that K/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.
From: Toby Gee [view email]
[v1]
Wed, 15 Aug 2012 19:04:24 UTC (45 KB)
[v2]
Sun, 10 Mar 2013 22:07:22 UTC (46 KB)
[v3]
Fri, 17 May 2013 07:56:19 UTC (45 KB)
[v4]
Wed, 18 Sep 2013 15:37:37 UTC (46 KB)
[v5]
Fri, 12 Jun 2026 10:15:39 UTC (55 KB)
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