Stable cohomology over local rings

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dc.creatorAvramov, Luchezar L.
dc.creatorVeliche, Oana
dc.date2005-07-31
dc.date2007-01-10
dc.date.accessioned2026-07-07T07:39:24Z
dc.date.available2026-07-07T07:39:24Z
dc.descriptionThe focus of this paper is on a poorly understood invariant of a commutative noetherian local ring $R$ with residue field $k$: the stable cohomology modules $\hat{Ext}^{n}_R(k,k)$, defined for each $n\in\mathbb{Z}$ by Benson and Carlson, Mislin, and Vogel; it coincides with Tate cohomology when $R$ is Gorenstein. It is proved that important properties of $R$, such as being regular, complete intersection, or Gorenstein, are detected by the $k$-rank of $\hat{Ext}^{n}_R(k,k)$ for an arbitrary $n\in\mathbb{Z}$. Such numerical characterizations are made possible by results on the structure of $\mathbb{Z}$-graded $k$-algebra carried by $\hat{Ext}^{n}_R(k,k)$. It is proved that in many cases this algebra is determined by the absolute cohomology algebra through a canonical homomorphism ${Ext}^{n}_R(k,k)\to\hat{Ext}^{n}_R(k,k)$.
dc.descriptionFinal version, to appear in Adv. Math. Major reorganization of the presentation. Many minor corrections
dc.identifierhttps://arxiv.org/abs/math/0508021
dc.identifierhttp://arxiv.org/abs/math/0508021
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/121436
dc.subjectCommutative Algebra
dc.subjectK-Theory and Homology
dc.subjectRepresentation Theory
dc.subject13D07; 13H10; 20J06
dc.titleStable cohomology over local rings
dc.typetext

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