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For questions on modules over rings.

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Is a reduced, torsion-free module of finite rank over an Henselian ring free?

Let $R$ be an Henselian discrete valuation ring with field of fractions $K$. Let $M$ be a torsion-free $R$-module of finite rank (i.e. $dim_K(M\otimes_RK)<+\infty$). Let $D$ be the maximal divisible $ …