Compactifications of s-arithmetic quotients for the projective general linear group

Takako Fukaya, Kazuya Kato, Romyar Sharifi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Let F be a global field, let S be a nonempty finite set ofplaces of F which contains the archimedean places of F, let d ≥ 1, and let X =v∈S Xv where Xv is the symmetric space (resp., Bruhat-Tits building) associated to PGLd (Fv) if v is archimedean (resp., non-archimedean). In this paper, we construct compactifications Γ\ ¯X of the quotient spaces Γ\X for S-arithmetic subgroups Γ of PGLd (F). The constructions make delicate use of the maximal Satake compactification of Xv (resp., the polyhedral compactification of Xv of Gérardin and Landvogt) for v archimedean (resp., non-archimedean). We also consider a variant of ¯X in which we use the standard Satake compactification of Xv (resp., the compactification of Xv due to Werner).

Original languageEnglish (US)
Title of host publicationElliptic Curves, Modular Forms and Iwasawa Theory
EditorsDavid Loeffler, Sarah Livia Zerbes
PublisherSpringer New York LLC
Pages161-223
Number of pages63
ISBN (Print)9783319450315
DOIs
StatePublished - 2016
EventConference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 - Cambridge, United Kingdom
Duration: Mar 25 2015Mar 27 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume188
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherConference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015
CountryUnited Kingdom
CityCambridge
Period3/25/153/27/15

Keywords

  • MSCs
  • Primary 14M25
  • Secondary 14F20

ASJC Scopus subject areas

  • Mathematics(all)

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