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Bicyclic algebras of prime exponent over function fields |
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| Authors: | Boris È . Kunyavskii Louis H. Rowen Sergey V. Tikhonov Vyacheslav I. Yanchevskii |
| Affiliation: | Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel ; Department of Mathematics, Bar-Ilan University, 52900 Ramat Gan, Israel ; Institute of Mathematics of the National Academy of Sciences of Belarus, ul. Surganova 11, 220072 Minsk, Belarus ; Institute of Mathematics of the National Academy of Sciences of Belarus, ul. Surganova 11, 220072 Minsk, Belarus |
| 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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