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

Takako Fukaya; Kazuya Kato; Romyar Sharifi

doi:10.1007/978-3-319-45032-2_5

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

Takako Fukaya, Kazuya Kato, Romyar Sharifi

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 X_v where X_v is the symmetric space (resp., Bruhat-Tits building) associated to PGL_d (F_v) 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 PGL_d (F). The constructions make delicate use of the maximal Satake compactification of X_v (resp., the polyhedral compactification of X_v 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 X_v (resp., the compactification of X_v due to Werner).

Original language	English (US)
Title of host publication	Elliptic Curves, Modular Forms and Iwasawa Theory
Editors	David Loeffler, Sarah Livia Zerbes
Publisher	Springer New York LLC
Pages	161-223
Number of pages	63
ISBN (Print)	9783319450315
DOIs	https://doi.org/10.1007/978-3-319-45032-2_5
State	Published - 2016
Externally published	Yes
Event	Conference 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 2015 → Mar 27 2015

Publication series

Name	Springer Proceedings in Mathematics and Statistics
Volume	188
ISSN (Print)	2194-1009
ISSN (Electronic)	2194-1017

Other

Other	Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015
Country/Territory	United Kingdom
City	Cambridge
Period	3/25/15 → 3/27/15

Keywords

MSCs
Primary 14M25
Secondary 14F20

ASJC Scopus subject areas

Mathematics(all)

Access to Document

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

Cite this

Compactifications of s-arithmetic quotients for the projective general linear group. / Fukaya, Takako; Kato, Kazuya; Sharifi, Romyar.

Elliptic Curves, Modular Forms and Iwasawa Theory. ed. / David Loeffler; Sarah Livia Zerbes. Springer New York LLC, 2016. p. 161-223 (Springer Proceedings in Mathematics and Statistics; Vol. 188).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Fukaya, T, Kato, K & Sharifi, R 2016, Compactifications of s-arithmetic quotients for the projective general linear group. in D Loeffler & SL Zerbes (eds), Elliptic Curves, Modular Forms and Iwasawa Theory. Springer Proceedings in Mathematics and Statistics, vol. 188, Springer New York LLC, pp. 161-223, Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 , Cambridge, United Kingdom, 3/25/15. https://doi.org/10.1007/978-3-319-45032-2_5

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

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