Torsion in tensor products, and tensor powers, of modules

2013/02/07 by Olgur Celikbas, Celikbas, Olgur, Srikanth B. Iyengar +5 · 2 citations
Mathematics · #13C40 #13D07 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C40 #msc:13D07

paper · pdf · doi:10.48550/arxiv.1302.1852

The results in this paper have been absorbed into arXiv:1412.6454 and arXiv:1412.6456

arxiv created 2014/12/22 · arxiv updated 2014/12/23

Abstract

For finitely generated modules M and N over a complete intersection R, the vanishing of Tor_i^R(M,N) for all i> 0 gives a tight relationship among depth properties of M, N and their tensor product. Here we concentrate on the converse and show, under mild conditions, that the tensor product of M and N being torsion-free (or satisfying higher Serre conditions) forces vanishing of Tor. Special attention is paid to the case of tensor powers of a single module.

Citations

• Torsion in tensor powers of modules
• Criteria for vanishing of Tor over Complete Intersections

Cited by

• Torsion in tensor powers of modules
• Criteria for vanishing of Tor over Complete Intersections

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• Torsion in tensor powers of modules
• Criteria for vanishing of Tor over Complete Intersections
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