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Submission: 2004, May 24
Let A be a central simple algebra over the field of rational functions in one variable over an arbitrary field of characteristic different from 2. If the Schur index of A is not divisible by the characteristic and its ramification locus has degree at most 3, then A is Brauer-equivalent to the tensor product of a quaternion algebra and a constant central division algebra D. The index of A is computed in terms of D and the ramification of A. The result is used to construct various examples of division algebras over rational function fields.
2000 Mathematics Subject Classification: Division algebra, Brauer group, rational functions, ramification
Keywords and Phrases: Division algebra, Brauer group, rational functions, ramification
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