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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Division algebras that ramify only on a plane quartic curve


Authors: Boris È. Kunyavskii, Louis H. Rowen, Sergey V. Tikhonov and Vyacheslav I. Yanchevskii
Journal: Proc. Amer. Math. Soc. 134 (2006), 921-929
MSC (2000): Primary 16K20
Published electronically: July 19, 2005
MathSciNet review: 2196022
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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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Additional Information

Boris È. Kunyavskii
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel
Email: kunyav@macs.biu.ac.il

Louis H. Rowen
Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel
Email: rowen@macs.biu.ac.il

Sergey V. Tikhonov
Affiliation: Institute of Mathematics of the National Academy of Sciences of Belarus, ul. Surganova 11, 220072 Minsk, Belarus
Email: tsv@im.bas-net.by

Vyacheslav I. Yanchevskii
Affiliation: Institute of Mathematics of the National Academy of Sciences of Belarus, ul. Surganova 11, 220072 Minsk, Belarus
Email: yanch@im.bas-net.by

DOI: http://dx.doi.org/10.1090/S0002-9939-05-08106-2
PII: S 0002-9939(05)08106-2
Received by editor(s): October 20, 2004
Published electronically: July 19, 2005
Additional Notes: The first author was partially supported by the Ministry of Absorption (Israel) and the Minerva Foundation through the Emmy Noether Research Institute of Mathematics.
The third and the fourth authors were partially supported by the Fundamental Research Foundation of Belarus.
This research was supported by the Israel Science Foundation founded by the Israel Academy of Sciences and Humanities — Center of Excellence Program and by RTN Network HPRN-CT-2002-00287.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.