Bicyclic algebras of prime exponent over function fields

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

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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).

Original languageEnglish
Pages (from-to)2579-2610
Number of pages32
JournalTransactions of the American Mathematical Society
Volume358
Issue number6
DOIs
StatePublished - Jun 2006

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