Ordinary parts and local-global compatibility at $\ell=p$

Bence Hevesi

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arXiv · 2311.13514

Ordinary parts and local-global compatibility at $\ell=p$

Bence Hevesi

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Abstract

We prove local-global compatibility results at $\ell=p$ for the torsion automorphic Galois representations constructed by Scholze, generalising the work of Caraiani--Newton. In particular, we verify, up to a nilpotent ideal, the local-global compatibility conjecture at $\ell=p$ of Gee--Newton in the case of imaginary CM fields under some technical assumptions. The key new ingredient is a local-global compatibility result for $Q$-ordinary self-dual automorphic representations for arbitrary parabolic subgroups.

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Bence Hevesi. 2023-11-22. Ordinary parts and local-global compatibility at $\ell=p$. https://arxiv.org/abs/2311.13514

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