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Galois Cohomology of Skew Fields and Brauer-Severi Varieties

This paper provides a comprehensive overview and synthesis of the deep connections between Galois cohomology, skew fields, and Brauer-Severi varieties, aiming to serve as an accessible reference for researchers and students seeking to understand these intertwined fields.
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Splitting unramified Brauer classes by abelian torsors and the period-index problem. [PDF]

Math Ann
Huybrechts D, Mattei D.
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XIIIth World Congress of Neurology. Hamburg, September 1-6, 1985. Abstracts. [PDF]

J Neurol, 1985
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The Brauer-Severi variety associated with a central simple algebra

, 2023
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Function fields of generalized brauer-severi varieties

Communications in Algebra, 1991
We define a generalized Brauer-Severi variety to be the projective Variety whose closed points correspond to rank m right ideals in a central simple algebra. We show that these varieties are forms of the Grassmann variety and their function fields are generic partial splitting fields for the associated algebras.
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Brauer-Severi varieties

Lecture Notes in Mathematics, 1982
M Artin, Artin M
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On the birational equivalence of Brauer-Severi varieties

Russian Mathematical Surveys, 1991
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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The Witt ring of a Brauer-Severi variety

manuscripta mathematica, 1998
The paper extends Arason's computation of the Witt ring of a projective space over a field [\textit{J. Kr. Arason}, Math. Ann. 253, 205-212 (1980; Zbl 0431.10011)] to twisted forms of projective spaces, i.e. Severi-Brauer varieties. Namely, it is proven that for a Severi-Brauer variety \(X/k\) the base-change homomorphism \(\sigma^{\ast} : W(k ...
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An extension of Arason's theorem to certain Brauer-Severi varieties

Archiv der Mathematik, 1998
\textit{J. K. Arason} [Math. Ann. 253, 205-212 (1980; Zbl 0437.10007)] proved that the Witt ring of a projective space over a field \(k\) of characteristic not two is isomorphic to the Witt ring of \(k\). The present author establishes a similar result in the case of Severi-Brauer varieties \(X\) associated with central simple \(k-\)algebras of odd ...
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