Matthew Brassil and Zinovy Reichstein: The Hermite-Joubert problem over p-fields,

Submission: 2015, Sep 10

Motivated by the classical theorems of Ch. Hermite and P. Joubert, we give a necessary and sufficient condition for an integer n, a field F_0 and a prime p to have the following property: for every etale algebra E/F of degree n, where F is a p-field containing F_0, there exists an element a in E such that F[a] = E and tr(a) = tr(a^p) = 0.

2010 Mathematics Subject Classification: 12F10, 14J70, 14G05

Keywords and Phrases: Hermite-Joubert problem, étale algebra, hypersurface, rational point, p-field

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