Frobenius powers of non-complete intersections

dc.creatorKantorovitz, Miriam Ruth
dc.date2001-06-27
dc.date2001-08-02
dc.date.accessioned2026-07-07T04:42:20Z
dc.date.available2026-07-07T04:42:20Z
dc.descriptionFor 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.descriptionLaTeX2e, 7 pages, uses pb-diagram
dc.identifierhttps://arxiv.org/abs/math/0106226
dc.identifierhttp://arxiv.org/abs/math/0106226
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/61735
dc.subjectCommutative Algebra
dc.titleFrobenius powers of non-complete intersections
dc.typetext

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