 Relative discriminant

ID: relative-discriminant

d_{L / K}

of a finite extension of number fields is the discriminant ideal of

O_{L}

over

O_{K}

. It satisfies

∣ d_{L} ∣ = ∣ d_{K} ∣^{[L : K]} N_{K / Q} (d_{L / K}),

and its prime divisors are exactly the ramified finite primes.

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