Quartic exercises
A correspondence between quartic étale algebras over a
field and quadratic étale extensions of cubic étale algebras is
set up and investigated. The basic constructions are laid out in general
for sets with a profinite group action and for torsors, and translated
in terms of étale algebras and Galois algebras. In the final section,
a parametrization of cyclic quartic algebras is given.
M.-A. Knus < knus@math.ethz.ch >
J.-P. Tignol < tignol@math.ucl.ac.be >