 Trivial Brauer group of a C1 field (source code)

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= Trivial Brauer group of a C1 field
{title2=$\operatorname{Br}(K)=0$}

A <central division algebra> of degree $d>1$ has an anisotropic <reduced norm> of degree $d$ in $d^2>d$ variables. That contradicts the <C1 field> property. Thus only degree one is possible, and every <central simple algebra> is split.

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