Tores associ\'es \`a une alg\`ebre \'etale quartique

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.