Geodesic
Constructions of Brauer-Severi Varieties and Norm Hypersurfaces
Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 230-238

Voir la notice de l'article provenant de la source Cambridge University Press

Let k be any field, A a central simple k-algebra of degree m (i.e., dimk A = m2). Several methods of constructing the generic splitting fields for A are proposed and Saltman proves that these methods result in almost the same generic splitting field [8, Theorems 4.2 and 4.4]. In fact, the generic splitting field constructed by Roquette [7] is the function field of the Brauer- Severi variety Vm(A) while the generic splitting field constructed by Heuser and Saltman [4 and 8] is the function field of the norm surface W(A). In this paper, to avoid possible confusion about the dimension, we shall call it the norm hypersurface instead of the norm surface. 
Kang, Ming-Chang. Constructions of Brauer-Severi Varieties and Norm Hypersurfaces. Canadian journal of mathematics, Tome 42 (1990) no. 2, pp. 230-238. doi: 10.4153/CJM-1990-013-7
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