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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.83.

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A classification of irreducible admissible mod $p$ representations of $p$-adic reductive groups
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by N. Abe, G. Henniart, F. Herzig and M.-F. Vignéras
J. Amer. Math. Soc. 30 (2017), 495-559
Published electronically: June 14, 2016


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.
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Bibliographic Information
  • N. Abe
  • Affiliation: Creative Research Institution (CRIS), Hokkaido University, N21, W10, Kita-ku, Sapporo, Hokkaido 001-0021, Japan
  • MR Author ID: 858099
  • Email:
  • G. Henniart
  • Affiliation: Laboratoire de Mathématiques d’Orsay, Université de Paris-Sud, Orsay cedex F-91405, France; CNRS, Orsay cedex F-91405, France
  • MR Author ID: 84385
  • Email:
  • F. Herzig
  • Affiliation: Department of Mathematics, University of Toronto, 40 St. George Street, Room 6290, Toronto, Ontario M5S 2E4, Canada
  • MR Author ID: 876324
  • Email:
  • M.-F. Vignéras
  • Affiliation: Institut de Mathématiques de Jussieu, 175 rue du Chevaleret, Paris 75013, France
  • Email:
  • Received by editor(s): December 6, 2014
  • Received by editor(s) in revised form: January 23, 2016, and May 3, 2016
  • Published electronically: June 14, 2016
  • Additional Notes: The first author was supported by JSPS KAKENHI Grant 26707001.
    The third author was partially supported by a Sloan Fellowship and an NSERC grant.
  • © Copyright 2016 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 30 (2017), 495-559
  • MSC (2010): Primary 22E50
  • DOI:
  • MathSciNet review: 3600042