TY - GEN

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

AU - Fukaya, Takako

AU - Kato, Kazuya

AU - Sharifi, Romyar

N1 - Funding Information:
The work of the first two authors was supported in part by the National Science Foundation under Grant No. 1001729. The work of the third author was partially supported by the National Science Foundation under Grant Nos. 1401122/1661568 and 1360583, and by a grant from the Simons Foundation (304824 to R.S.).
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

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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 -