Illinois Journal of Mathematics

Vanishing of Ext and Tor over some Cohen-Macaulay local rings

Craig Huneke, Adela N. Vraciu, and Liana M. Şega

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Abstract

We discuss vanishing of cohomology of finite modules over Cohen-Macaulay local rings $(R, \mathfrak m)$. Special attention is given to the case when the modules are annihilated by $\mathfrak m^2$. (Note that if $\mathfrak m^3=0$, then we can assume the modules satisfy this condition.) In this case we obtain effective versions of conjectures of Auslander-Reiten and Tachikawa.

Article information

Source
Illinois J. Math., Volume 48, Number 1 (2004), 295-317.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258136185

Digital Object Identifier
doi:10.1215/ijm/1258136185

Mathematical Reviews number (MathSciNet)
MR2048226

Zentralblatt MATH identifier
1043.13006

Subjects
Primary: 13D07: Homological functors on modules (Tor, Ext, etc.)
Secondary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

Citation

Huneke, Craig; Şega, Liana M.; Vraciu, Adela N. Vanishing of Ext and Tor over some Cohen-Macaulay local rings. Illinois J. Math. 48 (2004), no. 1, 295--317. doi:10.1215/ijm/1258136185. https://projecteuclid.org/euclid.ijm/1258136185


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