2005/01/11 by Willem A. de Graaf, de Graaf, Willem A., Michael Harrison +6
Engineering · Mathematics · #14Q10 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #math.AG #msc:14Q10
paper · pdf · doi:10.48550/arxiv.math/0501157
16 pages some minor revisions
openalex publication_date 2005/01/11 · arxiv created 2005/06/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.