Thin Severi-Brauer Varieties
(2011) Pure and Applied Mathematics Quarterly — Vol. 7, n° 3, p. 745-782 (2011)
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- Abstract
- 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 étale algebras. Similarly, thin quadrics are étale 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 étale algebras into central simple algebras (with or without involution), and consider the geometric counterpart of the Clifford algebra construction.
- Affiliations
Eidgenössische Technische Hochschule Zürich Departement Mathematik
Citations
Knus, M.-A., & Tignol, J.-P. (2011). Thin Severi-Brauer Varieties. Pure and Applied Mathematics Quarterly, 7(3), 745-782. https://doi.org/10.4310/PAMQ.2011.v7.n3.a7 (Original work published 2011)