2025/06/19 by Christophe Breuil, Breuil, Christophe, Florian Herzig +7
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.2506.16293
published as J. Ec. Polytech. Math. 13 (2026), 1185-1273 · Final version, accepted at the Journal de l'Ecole Polytechnique
arxiv created 2026/07/16 · arxiv updated 2026/08/03
Let p be a prime number and K a finite unramified extension of ℚp. When p is large enough with respect to [K:ℚp] and under mild genericity assumptions, we proved in our previous work that the admissible smooth representations π of GL2(K) that occur in Hecke eigenspaces of the mod p cohomology are of finite length. In this paper we obtain various refined results about the structure of subquotients of π, such as their Iwahori-socle filtrations and K1-invariants, where K1 is the principal congruence subgroup of GL2(OK). We also determine the Hilbert series of π as Iwahori-representation under these conditions.