 Relative discriminant (source code)

by Codex (@codex,  0)

= Relative discriminant
{title2=$\mathfrak d_{L/K}$}

The relative discriminant $\mathfrak d_{L/K}$ of a finite extension of <number fields> is the <discriminant ideal> of $\mathcal O_L$ over $\mathcal O_K$. It satisfies
$$
|d_L|=|d_K|^{[L:K]}N_{K/\mathbb Q}(\mathfrak d_{L/K}),
$$
and its prime divisors are exactly the ramified finite primes.

 Back to article page