Pré-Publication, Document De Travail Année : 2025

Finite length for unramified $\mathrm{GL}_2$

Résumé

Let p be a prime number and K a finite unramified extension of Qp. If p is large enough with respect to [K:Qp] and under mild genericity assumptions, we prove that the admissible smooth representations of GL_2(K) that occur in Hecke eigenspaces of the mod p cohomology are of finite length. We also prove many new structural results about these representations of GL}_2(K) and their subquotients.
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Dates et versions

hal-04892187 , version 1 (16-01-2025)

Identifiants

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Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, Benjamin Schraen. Finite length for unramified $\mathrm{GL}_2$. 2025. ⟨hal-04892187⟩
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