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1970•Mathematics of the USSR-IzvestiyaRequires access

BIRATIONAL PROPERTIES OF LINEAR ALGEBRAIC GROUPS

V E Voskresenskiĭ

Open publisher page 66 citations

Abstract

This paper investigates the question of birational equivalence of linear algebraic groups. Certain necessary conditions are derived for rationality of a group over the field of definition, which in application to algebraic tori are fairly delicate. In particular, it is shown that the condition is a necessary criterion of rationality for tori and for semisimple groups defined over an algebraic number field.

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What this paper is about

This paper investigates the question of birational equivalence of linear algebraic groups. Certain necessary conditions are derived for rationality of a group over the field of definition, which in application to algebraic tori are fairly delicate. In particular, it is shown that the condition is a necessary criterion of rationality for tori and for semisimple groups defined over an algebraic number field.

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OpenAlex reports 66 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

This paper investigates the question of birational equivalence of linear algebraic groups. Certain necessary conditions are derived for rationality of a group over the field of definition, which in application to algebraic tori are fairly delicate. In particular, it is shown that the condition is a necessary criterion of rationality for tori and for semisimple groups defined over an algebraic number field.

Key concepts: Mathematics, Pure mathematics, Algebraic number, Algebra over a field, Mathematical analysis

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