论文标题
研究刚性属性的研究
A study of the cohomological rigidity property
论文作者
论文摘要
在本文中，以卢克（Luk）和雅（Yau）的作品以及霍纳克（Huneke）和维加德（Wiegand）的作品的启发，我们研究了模块的张量产物的共同学刚性特性的各个方面，而不是合理的Noetherian戒指。我们确定了张量产品的单个局部共同体学模块消失的条件，意味着所有较低的产品的消失，并在张量产品的局部共同体学模块与泰特同源性之间获得新的联系。我们的论点对模块的张量产物的深度以及模块的freeness的标准产生了界限。一路上，我们还提供了平滑完整交集的矢量束的分裂标准。
In this paper, motivated by a work of Luk and Yau, and Huneke and Wiegand, we study various aspects of the cohomological rigidity property of tensor product of modules over commutative Noetherian rings. We determine conditions under which the vanishing of a single local cohomology module of a tensor product implies the vanishing of all the lower ones, and obtain new connections between the local cohomology modules of tensor products and the Tate homology. Our argument yields bounds for the depth of tensor products of modules, as well as criteria for freeness of modules over complete intersection rings. Along the way, we also give a splitting criteria for vector bundles on smooth complete intersections.
