Reductions of semi-stable representations using the Iwahori mod p Local Langlands Correspondence

2023/11/07 by Chitrao, Anand, Ghate, Eknath · 3 citations
#11F80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2311.03740

Abstract

We determine the mod p reductions of all two-dimensional semi-stable representations V_k,L of the Galois group of ℚ_p of weights 3 ≤ k ≤ p+1 and L-invariants L for primes p ≥ 5. In particular, we describe the constants appearing in the unramified characters completely. The proof involves computing the reduction of Breuil's GL₂(ℚ_p)-Banach space B(k,L), by studying certain logarithmic functions using background material developed by Colmez, and then applying an Iwahori theoretic version of the mod p Local Langlands Correspondence.

Cited by

• The semi-stable Local Langlands Correspondence
• Factorisation de la cohomologie de systèmes locaux p-adiques sur le demi-plan de Drinfeld
• Iwahori-Hecke model for the universal supersingular representation

Related

• The semi-stable Local Langlands Correspondence
• An Iwahori theoretic mod p Local Langlands Correspondence
• A semisimple mod p Langlands correspondence in families for GL₂(ℚ_p)
• Reduction modulo p of certain semi-stable representations
• Reductions of 2-dimensional semi-stable representations with large \mathcal L-invariant