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.
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