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A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces

Willem A. de Graaf·Michael Harrison·Jana Pilnikova·Josef Schicho
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Abstract

It is well-known that a Severi-Brauer surface has a rational point if and only if it is isomorphic to the projective plane. Given a Severi-Brauer surface, we study the problem to decide whether such an isomorphism to the projective plane, or such a rational point, does exist; and to construct such an isomorphism or such a point in the affirmative case. We give an algorithm using Lie algebra techniques. The algorithm has been implemented in Magma.

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Willem A. de Graaf, Michael Harrison, Jana Pilnikova, Josef Schicho. 2005-06-21. A Lie Algebra Method for Rational Parametrization of Severi-Brauer Surfaces. https://arxiv.org/abs/math/0501157

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