Frobenius powers of non-complete intersections
| dc.creator | Kantorovitz, Miriam Ruth | |
| dc.date | 2001-06-27 | |
| dc.date | 2001-08-02 | |
| dc.date.accessioned | 2026-07-07T04:42:20Z | |
| dc.date.available | 2026-07-07T04:42:20Z | |
| dc.description | For a commutative ring $R$ of characteristic $p$, let $ϕ: R \to R$ be the Frobenius homomorphism and let $^{ϕ^r}R$ denote the $R$-module structure on $R$ defined via the $r$-th power of the Frobenius. We show that the Tor functor against the Frobenius module, $\Tor^R_*(-, {^{ϕ^r}}R)$, is rigid for a certain class of depth zero rings which includes rings that are not complete intersection. We also show that $\Tor^R_*(-, {^{ϕ^r}}R)$ is not rigid (non-vacuously) when $\depth (R) >0$ and $r$ is large enough. This answers a question of Avramov and Miller: does rigidity of $\Tor^R_*(-, {^{ϕ^r}}R)$ hold for non-complete intersections? | |
| dc.description | LaTeX2e, 7 pages, uses pb-diagram | |
| dc.identifier | https://arxiv.org/abs/math/0106226 | |
| dc.identifier | http://arxiv.org/abs/math/0106226 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61735 | |
| dc.subject | Commutative Algebra | |
| dc.title | Frobenius powers of non-complete intersections | |
| dc.type | text |