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Pré-Publication, Document De Travail Année : 2022

GELFAND-KIRILLOV DIMENSION AND MOD p COHOMOLOGY FOR GL 2

Christophe Breuil
  • Fonction : Auteur
Florian Herzig
  • Fonction : Auteur
Yongquan Hu
  • Fonction : Auteur
Benjamin Schraen

Résumé

Let p be a prime number, F a totally real number field unramified at places above p and D a quaternion algebra of center F split at places above p and at no more than one infinite place. Let v be a fixed place of F above p and r : Gal(F /F) → GL2(Fp) an irreducible modular continuous Galois representation which, at the place v, is semisimple and sufficiently generic (and satisfies some weak genericity conditions at a few other finite places). We prove that many of the admissible smooth representations of GL2(Fv) over Fp associated to r in the corresponding Hecke-eigenspaces of the mod p cohomology have Gelfand-Kirillov dimension [Fv : Qp], as well as several related results. Contents
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Dates et versions

hal-03883840 , version 1 (04-12-2022)

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Christophe Breuil, Florian Herzig, Yongquan Hu, Stefano Morra, Benjamin Schraen. GELFAND-KIRILLOV DIMENSION AND MOD p COHOMOLOGY FOR GL 2. 2022. ⟨hal-03883840⟩

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