### 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) |
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Title of host publication | Elliptic Curves, Modular Forms and Iwasawa Theory |

Publisher | Springer New York LLC |

Pages | 161-223 |

Number of pages | 63 |

Volume | 188 |

ISBN (Print) | 9783319450315 |

DOIs | |

Publication status | 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 |

### Other

Other | Conference on Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John H. Coates, 2015 |
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Country | United Kingdom |

City | Cambridge |

Period | 3/25/15 → 3/27/15 |

### Fingerprint

### Keywords

- MSCs
- Primary 14M25
- Secondary 14F20

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Elliptic Curves, Modular Forms and Iwasawa Theory*(Vol. 188, pp. 161-223). Springer New York LLC. https://doi.org/10.1007/978-3-319-45032-2_5