Leopoldt theorem for abelian number fields
= Leopoldt theorem for abelian number fields
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The <Leopoldt conjecture> holds for every finite abelian extension of $\mathbb Q$. The proof uses linear independence of $p$-adic logarithms of algebraic numbers. In cyclotomic towers it supplies the ranks of the global-unit terms in the <class-field unit sequence>; it is not needed for the <unramified Iwasawa torsion theorem> in arbitrary towers.