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When are global units norms of units?

David Folk — 1996

Acta Arithmetica

Making sense of capitulation: reciprocal primes

David Folk — 2016

Acta Arithmetica

Let ℓ be a rational prime, K be a number field that contains a primitive ℓth root of unity, L an abelian extension of K whose degree over K, [L:K], is divisible by ℓ, a prime ideal of K whose ideal class has order ℓ in the ideal class group of K, and $a_{}$ any generator of the principal ideal $^{ℓ}$ . We will call a prime ideal of K ’reciprocal to ’ if its Frobenius element generates $G a l (K (\sqrt[ℓ]{a_{}}) / K)$ for every choice of $a_{}$ . We then show that becomes principal in L if and only if every reciprocal prime is not a norm inside...

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