论文标题
关于Huneke和Wiegand的猜想以及（CO）同源性的消失的评论
Remarks on a conjecture of Huneke and Wiegand and the vanishing of (co)homology
论文作者
论文摘要
在本文中，我们研究了Huneke和Wiegand的长期猜想，这与一维当地域的某些张量产品的扭曲量有关。我们利用Hochster的Theta不变性，并表明对两个周期性模块的猜想是正确的。我们还利用Orlov的结果，并制定了一种新条件，如果超过超脸环，则迫使Huneke和Wiegand的猜想在任意编辑的完整交叉点上是正确的。在途中，我们研究了模块的张量产物中Tate（CO）同源性消失（CO）同源性的消失之间的相互作用，并获得具有独立关注的新结果。
In this paper we study a long-standing conjecture of Huneke and Wiegand which is concerned with the torsion submodule of certain tensor products of modules over one-dimensional local domains. We utilize Hochster's theta invariant and show that the conjecture is true for two periodic modules. We also make use of a result of Orlov and formulate a new condition which, if true over hypersurface rings, forces the conjecture of Huneke and Wiegand to be true over complete intersection rings of arbitrary codimension. Along the way we investigate the interaction between the vanishing of Tate (co)homology and torsion in tensor products of modules, and obtain new results that are of independent interest.
