Leopoldt conjecture
= Leopoldt conjecture
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{title2=$\delta_{F,p}=0$}
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The Leopoldt conjecture says that the diagonal image of the global units of a <number field> in its local $p$-adic unit groups has $\mathbb Z_p$-rank $r_1+r_2-1$. A defect would measure a loss of rank after $p$-adic completion. It is a theorem for abelian extensions of $\mathbb Q$.