Adam Logan

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math.NT2026

Modular curves and bad reduction

Adam Logan, David McKinnon

We prove results that imply, under various hypotheses, that every elliptic curve over a number field $k$ corresponding to a point on a modular curve has bad reduction at a certain…

math.NT2024

The Basic Theory of Clifford-Bianchi Groups for Hyperbolic n-Space

Taylor Dupuy, Anton Hilado, Colin Ingalls +1

Let $K$ be a $Q$ -Clifford algebra associated to an $(n - 1)$ -ary positive definite quadratic form and let $O$ be a maximal order in $K$ . A Clifford-Bianchi group i…