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arXiv · 1510.00872

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

Takako Fukaya·Kazuya Kato·Romyar Sharifi
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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.

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Takako Fukaya, Kazuya Kato, Romyar Sharifi. 2015-10-03. Compactifications of S-arithmetic quotients for the projective general linear group. https://arxiv.org/abs/1510.00872

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