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Pré-Publication, Document De Travail Année : 2023

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

Résumé

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.
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Dates et versions

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

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