Tokyo Journal of Mathematics

Kummer Theories for Algebraic Tori and Normal Basis Problem

Noriyuki SUWA

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We discuss the inverse Galois problem with normal basis, concerning Kummer theories for algebraic tori, in the framework of group schemes. The unit group scheme of a group algebra plays an important role in this article, as was pointed out by Serre~[8]. We develop our argument not only over a field but also over a ring, considering integral models of Kummer theories for algebraic tori.

Article information

Tokyo J. Math., Volume 39, Number 3 (2017), 827-862.

First available in Project Euclid: 6 October 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 13B05: Galois theory
Secondary: 14L15: Group schemes 12G05: Galois cohomology [See also 14F22, 16Hxx, 16K50]


SUWA, Noriyuki. Kummer Theories for Algebraic Tori and Normal Basis Problem. Tokyo J. Math. 39 (2017), no. 3, 827--862. doi:10.3836/tjm/1475723092.

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