Principalization of ideals in abelian extensions of number fields

Details Principalization of ideals in abelian extensions of number fields Principalization of ideals in abelian extensions of number fields

2008-03-28

arxiv.org/abs/0803.4147v2

Mathematics

Number Theory

Scientific paper

We give the complete proof of a conjecture of Georges Gras which claims that,
for any extension $K/k$ of number fields in which at least one infinite place
is totally split, every ideal $I$ of $K$ principalizes in the compositum
$Kk^{ab}$ of $K$ with the maximal abelian extension $k^{ab}$ of $k$

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