# Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups

@inproceedings{ArenasCarmona2021QuotientsOT, title={Quotients of the Bruhat-Tits tree by arithmetic subgroups of special unitary groups}, author={Luis Arenas-Carmona and Claudio Bravo and Beno{\^i}t Loisel and Giancarlo Lucchini Arteche}, year={2021} }

Let K be the function field of a curve C over a field F of either odd or zero characteristic. Following the work by Serre and Mason on SL2, we study the action of arithmetic subgroups of SU(3) on its corresponding Bruhat-Tits tree associated to a suitable completion of K. More precisely, we prove that the quotient graph “looks like a spider”, in the sense that it is the union of a set of cuspidal rays (the “legs”), parametrized by an explicit Picard group, that are attached to a connected graph… Expand

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