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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Bicyclic algebras of prime exponent over function fields


Authors: Boris È. Kunyavskii, Louis H. Rowen, Sergey V. Tikhonov and Vyacheslav I. Yanchevskii
Journal: Trans. Amer. Math. Soc. 358 (2006), 2579-2610
MSC (2000): Primary 16K20
Published electronically: October 21, 2005
MathSciNet review: 2204045
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Abstract: We examine some properties of bicyclic algebras, i.e. the tensor product of two cyclic algebras, defined over a purely transcendental function field in one variable. We focus on the following problem: When does the set of local invariants of such an algebra coincide with the set of local invariants of some cyclic algebra? Although we show this is not always the case, we determine when it happens for the case where all degeneration points are defined over the ground field. Our main tool is Faddeev's theory. We also study a geometric counterpart of this problem (pencils of Severi-Brauer varieties with prescribed degeneration data).


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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/S0002-9947-05-03772-4
PII: S 0002-9947(05)03772-4
Received by editor(s): November 5, 2002
Received by editor(s) in revised form: June 21, 2004
Published electronically: October 21, 2005
Additional Notes: 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.
The first author was partially supported by the Ministry of Absorption (Israel), the Minerva Foundation through the Emmy Noether Research Institute of Mathematics, and INTAS 00-566.
The third and the fourth authors were partially supported by the Fundamental Research Foundation of Belarus, TMR ERB FMRX CT-97-0107, and INTAS 99-081.
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.