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On a conjecture of Auslander and Reiten

Craig Huneke·Graham Leuschke
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Abstract

In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that Ext^i_Lambda(M,M)=0 for all i \geq 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen--Macaulay normal domains containing the rational numbers, and slightly more generally.

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Craig Huneke, Graham Leuschke. 2003-07-16. On a conjecture of Auslander and Reiten. https://arxiv.org/abs/math/0305001

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