Zinovy Reichstein: Joubert's theorem fails in characteristic 2


Submission: 2014, Jun 29, updated: 2014, Aug 11

Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) is different from 2 then L is generated over K by an element whose minimal polynomial is of the form

t^6 + a t^4 + b t^2 + ct + d

for some a, b, c, d in K. We show that this theorem fails in characteristic 2.

2010 Mathematics Subject Classification: 12E10, 12F10

Keywords and Phrases: Sextic polynomial, Joubert's theorem, rational covariants, cubic hypersurface.

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