Explicit isomorphisms of quaternion algebras over quadratic global fields

Abstract

Let $L$ be a separable quadratic extension of either $\mathbb{Q}$ or ${\mathbb{F}}_q(t)$. We propose efficient algorithms for finding isomorphisms between quaternion algebras over $L$. Our techniques are based on computing maximal one-sided ideals of the corestriction of a central simple $L$-algebra.

arXiv comment22 pages, includes implementation, characteristic 2 results put in a separate paper arXiv:2203.04068