TY - GEN

T1 - Compactifications of s-arithmetic quotients for the projective general linear group

AU - Fukaya, Takako

AU - Kato, Kazuya

AU - Sharifi, Romyar

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016

PY - 2016

Y1 - 2016

N2 - 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).

AB - 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).

KW - MSCs

KW - Primary 14M25

KW - Secondary 14F20

UR - http://www.scopus.com/inward/record.url?scp=85025138014&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85025138014&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-45032-2_5

DO - 10.1007/978-3-319-45032-2_5

M3 - Conference contribution

AN - SCOPUS:85025138014

SN - 9783319450315

T3 - Springer Proceedings in Mathematics and Statistics

SP - 161

EP - 223

BT - Elliptic Curves, Modular Forms and Iwasawa Theory

A2 - Loeffler, David

A2 - Zerbes, Sarah Livia

PB - Springer New York LLC

T2 - Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015

Y2 - 25 March 2015 through 27 March 2015

ER -