3 citations · 5 across the 3 of their papers we have counts for
3 papers
math.RA2019★ 2 cited
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.RA2014★ 3 cited
Division algebras of prime degree with infinite genus
Sergey V. Tikhonov
The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D'] in the Brauer group Br(F), where D' is a central div…
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.