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Detecting completeness from ext-vanishing

Anders J. Frankild·Sean Sather-Wagstaff
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Abstract

Motivated by work of C. U. Jensen, R.-O. Buchweitz, and H. Flenner, we prove the following result. Let $R$ be a commutative Noetherian ring and $a$ an ideal in the Jacobson radical of $R$. Let $\hat{R}^a$ be the $a$-adic completion of $R$. If $M$ is a finitely generated $R$-module such that $\ext^i_R(\hat{R}^a,M)=0$ for all $i\neq 0$, then $M$ is $a$-adically complete.

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Anders J. Frankild, Sean Sather-Wagstaff. 2007-03-28. Detecting completeness from ext-vanishing. https://arxiv.org/abs/math/0606736

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