Criteria for vanishing of Tor over Complete Intersections
Criteria for vanishing of Tor over Complete Intersections
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DOI：
10.2140/pjm.2015.276.93
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Olgur Celikbas;S. Iyengar;Greg Piepmeyer;R. Wiegand
中科院分区：
文献类型：
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作者：
Olgur Celikbas;S. Iyengar;Greg Piepmeyer;R. Wiegand
本文利用Dao的eta-配对性质以及Huneke， Jorgensen和Wiegand的技术，研究了有限生成模M，N在完全相交上的Tor_i（M，N）的消失。在深度条件下，证明了所有正整数i在M， N及其张量积上Tor_i（M， N）的消失性。我们的论点改进了Dao的结果，并在Tor的消失和张量积的深度之间建立了新的联系。
In this paper we exploit properties of Dao's eta-pairing as well as techniques of Huneke, Jorgensen, and Wiegand to study the vanishing of Tor_i(M,N) of finitely generated modules M, N over complete intersections. We prove vanishing of Tor_i(M, N) for all positive integers i under depth conditions on M, N, and their tensor product. Our arguments improve a result of Dao and establish a new connection between the vanishing of Tor and the depth of tensor products.