Year: 2026
Type: preprint
Abstract: We prove the finiteness of the genus of quaternion division algebras over some formally real fields. In particular, if $F$ is a formally real field and the second power of the fundamental ideal $I^2(F)$ is torsion-free, then the genus of any quaternion division $F$-algebra is trivial. For instance, this immediately implies that the genus vanishes for any quaternion division algebra over a formally real pythagorean field. The proofs are based on methods from the theory of quadratic forms.
Source: arXiv (Cornell University)
Author: Tikhonov, Sergey V.
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220707345