论文标题
Cohen-Macaulay Burch戒指的消失（CO）同源性，FreeNess标准和Auslander-Reiten猜想
Vanishing of (co)homology, freeness criteria, and the Auslander-Reiten conjecture for Cohen-Macaulay Burch rings
论文作者
论文摘要
我们在（CO）同源性消失和延伸二元性方面建立了新的结果，并在Cohen-Macaulay本地环上得出了许多有限模块的Freeness标准。在主要应用中，我们解决了长期以来的奥斯兰德 - 里列顿猜想，用于Cohen-Macaulay Burch环类，除其他结果以及相关问题，例如Tachikawa和Huneke-Wiegand undencentures。我们还取得了进一步的关注主题的结果，例如张量产品的Cohen-MaCaulayness和Tor-Intiondictions，并受到Huneke和Leuschke的纸张的启发，我们获得了何时定期的局部环或完整的交叉点或Gorenstein的特征。对于常规案例，我们描述了一些经典差异问题的进度，例如Zariski-Lipman猜想的强大版本。一路上，我们从文献中概括了一些结果，并提出了各种问题。
We establish new results on (co)homology vanishing and Ext-Tor dualities, and derive a number of freeness criteria for finite modules over Cohen-Macaulay local rings. In the main application, we settle the long-standing Auslander-Reiten conjecture for the class of Cohen-Macaulay Burch rings, among other results toward this and related problems, e.g., the Tachikawa and Huneke-Wiegand conjectures. We also derive results on further topics of interest such as Cohen-Macaulayness of tensor products and Tor-independence, and inspired by a paper of Huneke and Leuschke we obtain characterizations of when a local ring is regular, or a complete intersection, or Gorenstein; for the regular case, we describe progress on some classical differential problems, e.g., the strong version of the Zariski-Lipman conjecture. Along the way, we generalize several results from the literature and propose various questions.
