The weight part of Serre's conjecture for GL(2)

Abstract

Let p > 2 be prime. We use purely local methods to determine the possible reductions of certain two-dimensional crystalline representations, which we call "pseudo-Barsotti-Tate representations", over arbitrary finite extensions of the p-adics. As a consequence, we establish (under the usual Taylor-Wiles hypothesis) the weight part of Serre's conjecture for GL(2) over arbitrary totally real fields.

41 pages. To appear, Forum of Mathematics, Pi

References in corpus (1)

• Lattices in the cohomology of Shimura curves

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