2 papers
math.RA2019
On genus of division algebras
Sergey V. Tikhonov
The genus of a finite-dimensional central division algebra over a field is defined as the collection of classes , where is a central division $…
math.AG2004
Division algebras that ramify only on a plane quartic curve
Boris E. Kunyavskii, Louis H. Rowen, Sergey V. Tikhonov +1
Let k be an algebraically closed field of characteristic 0. We prove that any division algebra over k(x,y) whose ramification locus lies on a quartic curve is cyclic.