Detecting completeness from ext-vanishing
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- June 2006
- DOI:
- 10.48550/arXiv.math/0606736
- arXiv:
- arXiv:math/0606736
- Bibcode:
- 2006math......6736F
- Keywords:
-
- Mathematics - Commutative Algebra;
- Mathematics - Rings and Algebras;
- 13B35;
- 13D07;
- 13D25;
- 13D45;
- 13J10
- E-Print:
- 10 pages