AI 中文总结
研究具有对偶复形的诺特环上同调有限复形 Ext 消失的广义对称性，通过额外同调条件扩展并统一局部戈伦斯坦环上相关对称结果，揭示对偶复形在其中的作用。
AI 中文摘要
阿夫拉莫夫和布赫维茨以及胡内克和约根森的基础工作分别在局部完全交和 AB 环上建立了 Ext 消失的对称结果。后来，一些作者在对相关模的额外同调假设下研究了局部戈伦斯坦环上 Ext 消失的对称性。在这项工作中，我们在对相关复形的额外同调条件下，为具有对偶复形的诺特环上的同调有限复形提供了 Ext 消失的广义对称性。本文的结果扩展并统一了先前在局部戈伦斯坦环上证明的关于 Ext 消失的几个对称结果，并表明对偶复形在这些结果中一直存在。
英文摘要
Foundational work by Avramov and Buchweitz, as well as by Huneke and Jorgensen, established symmetry results for the vanishing of Ext over local complete intersections and AB-rings, respectively. Later, several authors studied symmetry in the vanishing of Ext over local Gorenstein rings under additional homological assumptions on the modules involved. In this work, we provide a generalized symmetry in the vanishing of Ext for homologically finite complexes over a Noetherian ring with a dualizing complex, under additional homological conditions on the complexes involved. The results in this paper extend and unify several symmetry results on the vanishing of Ext previously proved over local Gorenstein rings and show that the dualizing complex has been hidden in these results.
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