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arxiv: 1704.04072 · v1 · pith:IPKS3MNPnew · submitted 2017-04-13 · 🧮 math.AC

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

classification 🧮 math.AC
keywords etalegroupalgebraarbitrarydegreedimensionhomomorphismsmultiplicative
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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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