Volume (2004) no. 99

Coefficient systems and supersingular representations of

{GL}_{2} (F)

Paskunas, Vytautas

Mémoires de la Société Mathématique de France, no. 99 (2004), 90 p.

Abstract
Résumé

Let $F$ be a non-Archimedean local field with the residual characteristic $p$ . We construct a “good” number of smooth irreducible ${\bar{𝐅}}_{p}$ -representations of ${GL}_{2} (F)$ , which are supersingular in the sense of Barthel and Livné. If $F = 𝐐_{p}$ then results of Breuil imply that our construction gives all the supersingular representations up to the twist by an unramified quasi-character. We conjecture that this is true for an arbitrary $F$ .

Soit $F$ un corps local non archimédien de caractéristique résiduelle $p$ . Nous construisons le « bon » nombre de ${\bar{𝐅}}_{p}$ -représentations lisses et irréductibles de ${GL}_{2} (F)$ qui sont supersingulières au sens de Barthel et Livné. Si $F = 𝐐_{p}$ , les résultats de Breuil impliquent alors que notre construction donne toutes les représentations supersingulières à la torsion près par un quasi-caractère non ramifié. Nous conjecturons que ceci reste vrai pour $F$ quelconque.

MR 2128381 | Zbl 1249.22010 | 3 citations in Numdam

DOI : https://doi.org/10.24033/msmf.412
Classification: 22E50
Keywords: Supersingular, mod

p

-representations

@book{MSMF_2004_2_99__1_0,
     author = {Paskunas, Vytautas},
     title = {Coefficient systems and supersingular representations of $\mathrm{GL}\_2(F)$},
     series = {M\'emoires de la Soci\'et\'e Math\'ematique de France},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {99},
     year = {2004},
     doi = {10.24033/msmf.412},
     zbl = {1249.22010},
     mrnumber = {2128381},
     language = {en},
     url = {http://www.numdam.org/item/MSMF_2004_2_99__1_0}
}

Paskunas, Vytautas. Coefficient systems and supersingular representations of $\mathrm{GL}_2(F)$. Mémoires de la Société Mathématique de France, Serie 2, , no. 99 (2004), 90 p. doi : 10.24033/msmf.412. http://www.numdam.org/item/MSMF_2004_2_99__1_0/

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