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Constructions of Brauer-Severi Varieties and Norm Hypersurfaces

Published online by Cambridge University Press:  20 November 2018

Ming-Chang Kang
Ming-Chang Kang*
Affiliation:
National Taiwan University, Taipei, Republic of China
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 2 , 01 April 1990 , pp. 230 - 238
Copyright
Copyright © Canadian Mathematical Society 1990

References

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