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An Iwahori theoretic mod
$p$ local Langlands correspondence
- Part of
-
- Journal:
- Canadian Mathematical Bulletin / Volume 68 / Issue 3 / September 2025
- Published online by Cambridge University Press:
- 17 February 2025, pp. 805-817
- Print publication:
- September 2025
-
- Article
- Export citation
-
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.
