Algebra & Number Theory

Congruences of parahoric group schemes

Radhika Ganapathy

Full-text: Access denied (no subscription detected)

However, an active subscription may be available with MSP at msp.org/ant.

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ant/1566353016

Digital Object Identifier
doi:10.2140/ant.2019.13.1475

Mathematical Reviews number (MathSciNet)
MR3994573

Zentralblatt MATH identifier
07103982

Subjects
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

Keywords
parahoric close local fields

Citation

Ganapathy, Radhika. Congruences of parahoric group schemes. Algebra Number Theory 13 (2019), no. 6, 1475--1499. doi:10.2140/ant.2019.13.1475. https://projecteuclid.org/euclid.ant/1566353016


Export citation

References

  • 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, https://tinyurl.com/conreduct.
  • 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.