English

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

Number Theory 2016-12-12 v2 Algebraic Geometry Group Theory

Abstract

Let F be a global field, and let S be a finite set of places of F containing all archimedean places. Consider the product X of the symmetric spaces and Bruhat-Tits buildings for PGL_d of the completions of F at archimedean and non-archimedean places in S, respectively. We construct compactifications of the quotient of X by S-arithmetic subgroups of PGL_d(F). The constructions make delicate use of reductive Borel-Serre spaces for archimedean places and polyhedral and seminorm compactifications at nonarchimedean places. We also briefly discuss a few potential applications of our compacifications.

Keywords

Cite

@article{arxiv.1510.00872,
  title  = {Compactifications of S-arithmetic quotients for the projective general linear group},
  author = {Takako Fukaya and Kazuya Kato and Romyar Sharifi},
  journal= {arXiv preprint arXiv:1510.00872},
  year   = {2016}
}

Comments

65 pages

R2 v1 2026-06-22T11:12:09.611Z