Algebra & Number Theory

Congruences of parahoric group schemes

Radhika Ganapathy

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Let F be a nonarchimedean local field and let T be a torus over F . With T N R denoting the Néron–Raynaud model of T , a result of Chai and Yu asserts that the model T N R × O F O F p F m is canonically determined by ( T r l ( F ) , Λ ) for l m , where T r l ( F ) = ( O F p F l , p F p F l + 1 , ϵ ) with ϵ denoting the natural projection of p F p F l + 1 on p F p F l , and Λ : = X ( T ) . In this article we prove an analogous result for parahoric group schemes attached to facets in the Bruhat–Tits building of a connected reductive group over F .

Article information

Algebra Number Theory, Volume 13, Number 6 (2019), 1475-1499.

Received: 6 November 2018
Revised: 16 April 2019
Accepted: 25 May 2019
First available in Project Euclid: 21 August 2019

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 22E50: Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Secondary: 11F70: Representation-theoretic methods; automorphic representations over local and global fields

parahoric close local fields


Ganapathy, Radhika. Congruences of parahoric group schemes. Algebra Number Theory 13 (2019), no. 6, 1475--1499. doi:10.2140/ant.2019.13.1475.

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  • A.-M. Aubert, P. Baum, R. Plymen, and M. Solleveld, “The local Langlands correspondence for inner forms of ${\rm SL}_n$”, Res. Math. Sci. 3 (2016), art. id. 32.
  • A. I. Badulescu, “Correspondance de Jacquet–Langlands pour les corps locaux de caractéristique non nulle”, Ann. Sci. École Norm. Sup. $(4)$ 35:5 (2002), 695–747.
  • S. Bosch, W. Lütkebohmert, and M. Raynaud, Néron models, Ergebnisse der Mathematik $($3$)$ 21, Springer, 1990.
  • F. Bruhat and J. Tits, “Groupes réductifs sur un corps local”, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5–251.
  • F. Bruhat and J. Tits, “Groupes réductifs sur un corps local, II: Schémas en groupes, existence d'une donnée radicielle valuée”, Inst. Hautes Études Sci. Publ. Math. 60 (1984), 197–376.
  • C.-L. Chai and J.-K. Yu, “Congruences of Néron models for tori and the Artin conductor”, Ann. of Math. $(2)$ 154:2 (2001), 347–382.
  • B. Conrad, “Reductive group schemes”, preprint, SGA3 Summer School, 2011,
  • S. DeBacker and M. Reeder, “Depth-zero supercuspidal $L$-packets and their stability”, Ann. of Math. $(2)$ 169:3 (2009), 795–901.
  • P. Deligne, “Les corps locaux de caractéristique $p$, limites de corps locaux de caractéristique $0$”, pp. 119–157 in Representations of reductive groups over a local field, Hermann, Paris, 1984.
  • R. Ganapathy, “The local Langlands correspondence for ${\rm GSp}_4$ over local function fields”, Amer. J. Math. 137:6 (2015), 1441–1534.
  • R. Ganapathy and S. Varma, “On the local Langlands correspondence for split classical groups over local function fields”, J. Inst. Math. Jussieu 16:5 (2017), 987–1074.
  • T. Haines and M. Rapoport, “Appendix: On parahoric subgroups”, 2008. Appendix to G. Pappas and M. Rapoport, “Twisted loop groups and their affine flag varieties”, Adv. Math. 219:1 (2008), 118–198.
  • R. Howe, Harish-Chandra homomorphisms for $p$-adic groups, CBMS Regional Conf. Series in Math. 59, Amer. Math. Soc., Providence, RI, 1985.
  • D. Kazhdan, “Representations of groups over close local fields”, J. Analyse Math. 47 (1986), 175–179.
  • R. Kottwitz, “${\rm B}(G)$ for all local and global fields”, preprint, 2014.
  • E. Landvogt, A compactification of the Bruhat–Tits building, Lecture Notes in Math. 1619, Springer, 1996.
  • B. Lemaire, “Représentations génériques de ${\rm GL}_N$ et corps locaux proches”, J. Algebra 236:2 (2001), 549–574.
  • J.-P. Serre, Local fields, Graduate Texts in Math. 67, Springer, 1979.
  • R. Steinberg, “Regular elements of semisimple algebraic groups”, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 49–80.