Ordinary local representations and $\Ext$ groups

Debargha Banerjee; Srijan Das

paper

Ordinary local representations and $\Ext$ groups

arXiv:2210.02238

Abstract

We can associate an admissible unitary representation $I^(I ¨ _{p})$ of $\GL_2(\Q_p)$ with every local Galois representation $I ¨ _{p}$ by the $p$ -adic local Langlands correspondence. If $I ¨ _{p}$ is ordinary, we prove local and global vanishing results for $\Ext$ functors with respect to these representations.

Error in the proof of the main theorem. Result generalized with corrected proof in arXiv:2601.07707 [math.NT]