Sergey V. Tikhonov

activity

20232026

collaborators

3 papers

math.RA2026

Genus of quaternion algebras over formally real fields

Sergey V. Tikhonov

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 fund…

math.RA2024

Genus of division algebras over fields with infinite transcendence degree

Sergey V. Tikhonov

We prove the finiteness of the genus of finite-dimensional division algebras over many infinitely generated fields. More precisely, let $K$ be a finite field extension of a field w…

math.RA2023

Outer forms of type $A_{2}$ with infinite genus

Sergey V. Tikhonov

Let $G$ be an absolutely almost simple algebraic group over a field $K$ . The genus $gen_{K} (G)$ of $G$ is the set of $K$ -isomorphism classes of $K$ -forms $G^{'}$ of $G$ that have…

Genus of quaternion algebras over formally real fields

Genus of division algebras over fields with infinite transcendence degree

Outer forms of type A2​ with infinite genus

Outer forms of type $A_{2}$ with infinite genus