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Division algebras that ramify only on a plane quartic curve

Boris E. Kunyavskii·Louis H. Rowen·Sergey V. Tikhonov·Vyacheslav I. Yanchevskii
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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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Boris E. Kunyavskii, Louis H. Rowen, Sergey V. Tikhonov, Vyacheslav I. Yanchevskii. 2004-10-25. Division algebras that ramify only on a plane quartic curve. https://arxiv.org/abs/math/0410524

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