High Quality Content by WIKIPEDIA articles! In mathematics, a Severi-Brauer variety over a field K is an algebraic variety V which becomes isomorphic to projective space over an algebraic closure of K. Examples are conic sections C: provided C is non-singular, it becomes isomorphic to the projective line over any extension field L over which C has a point defined. The name is for Francesco Severi and Richard Brauer. Such varieties are of interest not only in diophantine geometry, but also in Galois cohomology.

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