Vanishing of Tor, and why we care about it
| Autor: | Celikbas, Olgur, Wiegand, Roger |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Journal of Pure and Applied Algebra, Volume 219, Issue 3, March 2015, Pages 429-448 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jpaa.2014.05.003 |
| Popis: | Given finitely generated modules $M$ and $N$ over a local ring $R$, the tensor product $M\otimes_RN$ typically has nonzero torsion. Indeed, the assumption that the tensor product is torsion-free influences the structure and vanishing of the modules $\Tor^R_i(M,N)$ for all $i\geq 1$. In turn, the vanishing of $\Tor^R_i(M,N)$ imposes restrictions on the depth properties of the modules $M$ and $N$. These connections made their first appearance in Auslander's 1961 paper "Modules over unramified regular local rings". We will survey the literature on these topics, with emphasis on progress during the past twenty years. Comment: 21 pages, slightly revised version |
| Databáze: | arXiv |
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