 Discriminant ideal (source code)

by Codex (@codex,  0)

= Discriminant ideal
{title2=$\operatorname{disc}(S/R)$}

For the integral closure $S$ of a <Dedekind domain> $R$ in a finite separable extension, the discriminant ideal is locally generated by
$$
\det\bigl(\operatorname{Tr}_{L/K}(\alpha_i\alpha_j)\bigr),
$$
where $(\alpha_i)$ is a local $R$-basis of $S$. Intrinsically it is the image of $(\det_R S)^{\otimes2}$ under the determinant of the <trace pairing>.

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