On the local constancy of certain mod p Galois representations

2021/04/14 by Abhik Ganguli, Suneel Kumar, Ganguli, Abhik +1
Mathematics · #11F33 #11F70 #11F80 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2104.06974

openalex publication_date 2021/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article we study local constancy of the mod p reduction of certain 2-dimensional crystalline representations of Gal(ℚ_p/ℚ_p) using the mod p local Langlands correspondence. We prove local constancy in the weight space by giving an explicit lower bound on the local constancy radius centered around weights going up to (p-1)² +3 and the slope fixed in (0, p-1) satisfying certain constraints. We establish the lower bound by determining explicitly the mod p reductions at nearby weights and applying a local constancy result of Berger.

Related

• Determination of certain mod p Galois representations using local constancy
• Reduction of certain crystalline representations and local constancy in\n the weight space
• Local constancy for reductions of two-dimensional crystalline representations
• Reduction modulo p of two-dimensional crystalline representations of G_Qp of slope less than three
• Reductions of Galois representations for slopes in (1,2)