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arXiv · 2311.02919

An Iwahori theoretic mod $p$ Local Langlands Correspondence

Anand Chitrao
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Abstract

We extend a comparison theorem of Anandavardhanan-Borisagar between the quotient of the induction of a mod $p$ character by the image of an Iwahori-Hecke operator and compact induction of a weight to the case of the trivial character. This involves studying the corresponding non-commutative Iwahori-Hecke algebra. We use this to give an Iwahori theoretic reformulation of the (semi-simple) mod $p$ Local Langlands Correspondence discovered by Breuil and reformulated functorially by Colmez. This version of the correspondence is expected to have applications to computing the mod $p$ reductions of semi-stable Galois representations.

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BibTeXRIS

Anand Chitrao. 2023-11-06. An Iwahori theoretic mod $p$ Local Langlands Correspondence. https://doi.org/10.4153/s0008439524000444

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