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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Dirichlet's unit theorem for reductive schemes

Let $O_{K,S}$ be the ring of $S$-integers in a number field $K$. Dirichlet's unit theorem implies that the group of units in $O_{K,S}$ is a finitely generated group. In other words, the group $\mathbb …
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