Geodesic
A classification of irreducible admissible mod 𝑝 representations of 𝑝-adic reductive groups
Abe, N.1 ; Henniart, G.2 ; Herzig, F.3 ; Vignéras, M.-F.4
1 Creative Research Institution (CRIS), Hokkaido University, N21, W10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
2 Laboratoire de Mathématiques d’Orsay, Université de Paris-Sud, Orsay cedex F-91405, France; CNRS, Orsay cedex F-91405, France
3 Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, Ontario M5S 2E4, Canada
4 Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, Paris 75013, France
Journal of the American Mathematical Society, Tome 30 (2017) no. 2, pp. 495-559

Voir la notice de l'article provenant de la source American Mathematical Society

Let $F$ be a locally compact non-archimedean field, $p$ its residue characteristic, and $\textbf {G}$ a connected reductive group over $F$. Let $C$ be an algebraically closed field of characteristic $p$. We give a complete classification of irreducible admissible $C$-representations of $G=\mathbf {G}(F)$, in terms of supercuspidal $C$-representations of the Levi subgroups of $G$, and parabolic induction. Thus we push to their natural conclusion the ideas of the third author, who treated the case $\mathbf {G}=\mathrm {GL}_m$, as further expanded by the first author, who treated split groups $\mathbf {G}$. As in the split case, we first get a classification in terms of supersingular representations of Levi subgroups, and as a consequence show that supersingularity is the same as supercuspidality.
DOI : 10.1090/jams/862

Abe, N. 1 ; Henniart, G. 2 ; Herzig, F. 3 ; Vignéras, M.-F. 4

1 Creative Research Institution (CRIS), Hokkaido University, N21, W10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
2 Laboratoire de Mathématiques d’Orsay, Université de Paris-Sud, Orsay cedex F-91405, France; CNRS, Orsay cedex F-91405, France
3 Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, Ontario M5S 2E4, Canada
4 Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, Paris 75013, France 
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Abe, N.; Henniart, G.; Herzig, F.; Vignéras, M.-F. A classification of irreducible admissible mod 𝑝 representations of 𝑝-adic reductive groups. Journal of the American Mathematical Society, Tome 30 (2017) no. 2, pp. 495-559. doi: 10.1090/jams/862

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