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

DOI:
https://doi.org/10.1090/S0002-9939-05-08106-2

Published electronically:
July 19, 2005

MathSciNet review:
2196022

Full-text PDF

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Abstract: Let be an algebraically closed field of characteristic 0. We prove that any division algebra over 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:
https://doi.org/10.1090/S0002-9939-05-08106-2

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.