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Ordinary local representations and $\Ext$ groups (2210.02238v3)
Published 5 Oct 2022 in math.NT
Abstract: We can associate an admissible unitary representation $\Pi(\rho_p)$ of $\GL_2(\Q_p)$ with every local Galois representation $\rho_p$ by the $p$-adic local Langlands correspondence. If $\rho_p$ is ordinary, we prove local and global vanishing results for $\Ext$ functors with respect to these representations.
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