The p-arithmetic homology of mod p representations of GL₂(ℚ_p)

2023/01/25 by Tarrach, Guillem
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2301.10676

Abstract

We compute the non-Eisenstein systems of Hecke eigenvalues contributing to the p-arithmetic homology of irreducible smooth mod p representations π of GL₂(ℚ_p) and to the cohomology of their duals. We show that in most cases they are associated to odd irreducible 2-dimensional Galois representations whose local component at p corresponds under the mod p local Langlands correspondence to a smooth representation that contains π as a subrepresentation.

Related

• On the mod p cohomology for GL₂
• On non-admissible irreducible modulo p representations of GL₂(ℚ_p²)
• A semisimple mod p Langlands correspondence in families for GL₂(ℚ_p)
• Multiplicities in the ordinary part of mod p cohomology for GL_n(ℚ_p)
• Images of Galois representations in mod p Hecke algebras