Tokyo Journal of Mathematics

Kummer Theories for Algebraic Tori and Normal Basis Problem

Noriyuki SUWA

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Abstract

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

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

Dates
First available in Project Euclid: 6 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1475723092

Digital Object Identifier
doi:10.3836/tjm/1475723092

Mathematical Reviews number (MathSciNet)
MR3634295

Zentralblatt MATH identifier
06727288

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

Citation

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. https://projecteuclid.org/euclid.tjm/1475723092


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References

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