Trees, quaternion algebras and modular curves
Mihran Papikian

TL;DR
This paper explores the action of unit groups of maximal orders in quaternion algebras over function fields on Bruhat-Tits trees, with applications to arithmetic geometry and group theory.
Contribution
It introduces new insights into the structure of quaternion algebra unit groups and their actions on Bruhat-Tits trees over function fields.
Findings
Characterization of unit group actions on Bruhat-Tits trees
Applications to arithmetic geometry involving modular curves
Connections to group theory via quaternion algebra structures
Abstract
We study the action on the Bruhat-Tits tree of unit groups of maximal orders in certain quaternion algebras over and discuss applications to arithmetic geometry and group theory.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometric and Algebraic Topology
