This article is cited in 11 papers

Rationality of certain algebraic tori

V. E. Voskresenskii


Abstract: It is shown that the necessary condition for pure transcendence of a field of invariants given by Swan is also sufficient. We prove the rationality of factors of the type $T/G_m$, where $T$ the are tori of a certain special form, as well as the extension of the statement $H^1(k,\operatorname{Pic}\overline V)=0$ to all connected linear groups with cyclic algebraic splitting field.

UDC: 513.6

MSC: Primary 12F20; Secondary 14C20, 20G99

Received: 03.02.1971

 English version: Mathematics of the USSR-Izvestiya, 1971, 5:5, 1049–1056

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