An Iwahori theoretic mod $p$ Local Langlands Correspondence

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.

References in corpus (3)

• Explicit reduction modulo p of certain 2-dimensional crystalline representations, II
• Reduction of Galois Representations of slope 1
• Reductions of Galois representations of Slope $\frac{3}{2}$

Cited by in corpus (1)

• Semi-stable representations as limits of crystalline representations