Ordinary local representations and $\Ext$ groups

Debargha Banerjee; Srijan Das

Ordinary local representations and $\Ext$ groups

Number Theory 2026-05-18 v4

Authors: Debargha Banerjee , Srijan Das

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.

Keywords

galois representations langlands correspondence automorphic representations

Cite

@article{arxiv.2210.02238,
  title  = {Ordinary local representations and $\Ext$ groups},
  author = {Debargha Banerjee and Srijan Das},
  journal= {arXiv preprint arXiv:2210.02238},
  year   = {2026}
}

Comments

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

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