Division algebras that ramify only on a plane quartic curve

Kunyavskiĭ, Boris; Rowen, Louis; Tikhonov, Sergey; Yanchevskiĭ, Vyacheslav

doi:10.1090/S0002-9939-05-08106-2

Division algebras that ramify only on a plane quartic curve
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by Boris È. Kunyavskiĭ, Louis H. Rowen, Sergey V. Tikhonov and Vyacheslav I. Yanchevskiĭ PDF

Proc. Amer. Math. Soc. 134 (2006), 921-929 Request permission

Abstract:

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.

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