Surjectivity of reduced norms over C2 fields
= Surjectivity of reduced norms over C2 fields
{title2=$\operatorname{Nrd}(D)=K$}
For a <central division algebra> $D$ of degree $d$ over a <C2 field>, the form $\operatorname{Nrd}(X)-aT^d$ has degree $d$ in $d^2+1$ variables. Its nontrivial zero must have $T\ne0$, because the <reduced norm> of a <division algebra> is anisotropic. Dividing $X$ by $T$ gives norm $a$. Zero is the norm of zero.