Geodesic
THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$
Forum of Mathematics, Pi, Tome 3 (2015)

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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 $\mathbb{Q}_{p}$. As a consequence, we establish (under the usual Taylor–Wiles hypothesis) the weight part of Serre’s conjecture for $\text{GL}(2)$ over arbitrary totally real fields. 
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     title = {THE {WEIGHT} {PART} {OF} {SERRE{\textquoteright}S} {CONJECTURE} {FOR} $\text{GL}(2)$},
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TOBY GEE; TONG LIU; DAVID SAVITT. THE WEIGHT PART OF SERRE’S CONJECTURE FOR $\text{GL}(2)$. Forum of Mathematics, Pi, Tome 3 (2015). doi: 10.1017/fmp.2015.1

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