Non-arithmetic uniformization of metric spaces attached to unitary Shimura varieties - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2023

Non-arithmetic uniformization of metric spaces attached to unitary Shimura varieties

Abstract

We construct non-arithmetic lattices in $PO(n,1)$ for each integer $n$ greater than one. To do so, we provide a construction of glueing together complete real hyperbolic orbifolds along totally geodesic subspaces. The hyperbolic orbifolds that we glue are those that arise from anti-unitary involutions on a unitary Shimura variety. This construction generalizes a method of Allcock-Carlson-Toledo, who glued hyperbolic quotient spaces in dimensions two, three and four.
Fichier principal
Vignette du fichier
main8.pdf (566.14 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-04003088 , version 1 (23-02-2023)

Identifiers

Cite

Olivier de Gaay Fortman. Non-arithmetic uniformization of metric spaces attached to unitary Shimura varieties. 2023. ⟨hal-04003088⟩
9 View
0 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More