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An Iwahori theoretic mod $p$ local Langlands correspondence

Part of: Linear algebraic groups and related topics Lie groups

Published online by Cambridge University Press:  17 February 2025

Anand Chitrao Open the ORCID record for Anand Chitrao [Opens in a new window]
Anand Chitrao*
Affiliation:
School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India e-mail: anandudaychitrao@hri.res.in
*
e-mail: anandchitrao@gmail.com
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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.

Keywords

Iwahorilocal Langlands correspondenceHecke algebramod p

MSC classification

Primary: 20G05: Representation theory
Secondary: 22E50: Representations of Lie and linear algebraic groups over local fields
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 13
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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References

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