Wild primes of a self-equivalence of a number field
Let K be a number field. Assume that the 2-rank of the ideal class group of K is equal to the 2-rank of the narrow ideal class group of K. Moreover, assume K has a unique dyadic prime and the class of is a square in the ideal class group of K. We prove that if ₁,...,ₙ are finite primes of K such that ∙ the class of is a square in the ideal class group of K for every i ∈ 1,...,n, ∙ -1 is a local square at for every nondyadic , then ₁,...,ₙ is the wild set of some self-equivalence of the field...