Division algebras that ramify only on a plane quartic curve

Boris È Kunyavskiǐ; Louis H. Rowen; Sergey V. Tikhonov; Vyacheslav I. Yanchevskiǐ

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

Division algebras that ramify only on a plane quartic curve

Boris È Kunyavskiǐ
, Louis H. Rowen
, Sergey V. Tikhonov
, Vyacheslav I. Yanchevskiǐ

Department of Mathematics

Belarus Academy of Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

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.

Original language	English
Pages (from-to)	921-929
Number of pages	9
Journal	Proceedings of the American Mathematical Society
Volume	134
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-05-08106-2
State	Published - Apr 2006

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title = "Division algebras that ramify only on a plane quartic curve",

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.",

author = "Kunyavskiǐ, \{Boris {\`E}\} and Rowen, \{Louis H.\} and Tikhonov, \{Sergey V.\} and Yanchevskiǐ, \{Vyacheslav I.\}",

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AU - Kunyavskiǐ, Boris È

AU - Rowen, Louis H.

AU - Tikhonov, Sergey V.

AU - Yanchevskiǐ, Vyacheslav I.

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N2 - 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.

AB - 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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Division algebras that ramify only on a plane quartic curve

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