Tores associés à une algèbre étale quartique
arXiv:1704.04072 · doi:10.1016/j.jpaa.2017.02.016
Abstract
Homomorphisms are defined between the multiplicative group of an etale algebra of dimension 4 and the multiplicative group of a canonically associated etale algebra of degree 6 over an arbitrary field. These homomorphisms are used to relate various norm groups and to describe the 2-torsion in the relative Brauer group of a separable extension of degree 4. Several remarkable properties of biquadratic extensions are thus extended to arbitrary etale algebras of dimension 4.
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