  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.
