We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over $\mathbb{F}_q(T)$ and discuss applications to arithmetic geometry and group theory.
Regular models of modular curves in prime level over ${\mathbb Z}_p^{\mathrm{ur}}$
Splitting of primes in number fields generated by points on some modular curves
Genus formula for modular curves of $D$-elliptic sheaves
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