Asymptotic behavior of Tor over complete intersections and applications
| dc.creator | Dao, Hailong | |
| dc.date | 2007-10-31 | |
| dc.date.accessioned | 2026-07-07T08:39:41Z | |
| dc.date.available | 2026-07-07T08:39:41Z | |
| dc.description | Let $R$ be a local complete intersection and $M,N$ are $R$-modules such that $\ell(\Tor_i^R(M,N))<\infty$ for $i\gg 0$. Imitating an approach by Avramov and Buchweitz, we investigate the asymptotic behavior of $\ell(\Tor_i^R(M,N))$ using Eisenbud operators and show that they have well-behaved growth. We define and study a function $η^R(M,N)$ which generalizes Serre's intersection multiplicity $χ^R(M,N)$ over regular local rings and Hochster's function $θ^R(M,N)$ over local hypersurfaces. We use good properties of $η^R(M,N)$ to obtain various results on complexities of $\Tor$ and $\Ext$, vanishing of $\Tor$, depth of tensor products, and dimensions of intersecting modules over local complete intersections. | |
| dc.identifier | https://arxiv.org/abs/0710.5818 | |
| dc.identifier | http://arxiv.org/abs/0710.5818 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/141157 | |
| dc.subject | Commutative Algebra | |
| dc.title | Asymptotic behavior of Tor over complete intersections and applications | |
| dc.type | text |