Abstract
Let${\rm\Pi}$be an irreducible unitary completion of a locally algebraic$\text{GL}_{2}(\mathbf{Q}_{p})$-representation. We describe those first-order deformations of${\rm\Pi}$which are themselves completions of a locally algebraic representation. This answers a question of Paškūnas and has direct applications to the Breuil–Mézard conjecture.
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