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Answer by Vadim Alekseev for Is there a gap or flaw in Lang's proof of...

I think what is meant here is indeed not a monic polynomial over $\mathbb Z$, but rather one whose coefficients are (jointly) coprime. This, of course, is uniquely determined by the minimal polynomial...

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Is there a gap or flaw in Lang's proof of Dirichlet's $S$-units theorem?

Here is an apparent gap in a discreteness result of Lang that is a preliminary step in his proof of Dirichlet’s $S$-unit theorem. I have been working on a Minkowski-free approach to algebraic number...

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