%0 Journal Article
%T Thin Severi-Brauer Varieties
%A Max-Albert Knus
%A Jean-Pierre Tignol
%J Mathematics
%D 2009
%I arXiv
%X Severi-Brauer varieties are twisted forms of projective spaces (in the sense of Galois cohomology) and are associated in a functorial way to central simple algebras. Similarly quadrics are related to algebras with involution. Since thin projective spaces are finite sets, thin Severi-Brauer varieties are finite sets endowed with a Galois action; they are associated to etale algebras. Similarly, thin quadrics are etale algebras with involution. We discuss embeddings of thin Severi-Brauer varieties and thin quadrics in Severi-Brauer varieties and quadrics as geometric analogues of embeddings of etale algebras into central simple algebras (with or without involution), and consider the geometric counterpart of the Clifford algebra construction.
%U http://arxiv.org/abs/0912.3359v1