Loterre: Mathematics: Severi-Brauer variety

geometry > algebraic geometry > Diophantine geometry > Severi-Brauer variety

number > number theory > Diophantine geometry > Severi-Brauer variety

algebra > abstract algebra > algebraic structure > homological algebra > Severi-Brauer variety

geometry > algebraic geometry > algebraic variety > algebraic group > Severi-Brauer variety

Severi-Brauer variety

In mathematics, a Severi–Brauer variety over a field K is an algebraic variety V which becomes isomorphic to a projective space over an algebraic closure of K. The varieties are associated to central simple algebras in such a way that the algebra splits over K if and only if the variety has a rational point over K. Francesco Severi (1932) studied these varieties, and they are also named after Richard Brauer because of their close relation to the Brauer group.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Severi%E2%80%93Brauer_variety)

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