## Classification of the Tor-algebras of codimension four almost complete intersections

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- by Andrew R. Kustin PDF
- Trans. Amer. Math. Soc.
**339**(1993), 61-85 Request permission

## Abstract:

Let $(R,m,k)$ be a local ring in which $2$ is a unit. Assume that every element of $k$ has a square root in $k$. We classify the algebras $\operatorname {Tor}_ \bullet ^R(R/J,k)$ as $J$ varies over all grade four almost complete intersection ideals in $R$ . The analogous classification has already been found when $J$ varies over all grade four Gorenstein ideals [21], and when $J$ varies over all ideals of grade at most three [5, 30]. The present paper makes use of the classification, in [21], of the Tor-algebras of codimension four Gorenstein rings, as well as the (usually nonminimal) ${\text {DG}}$-algebra resolution of a codimension four almost complete intersection which is produced in [25 and 26].## References

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## Additional Information

- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**339**(1993), 61-85 - MSC: Primary 13D03; Secondary 13C05, 13C40
- DOI: https://doi.org/10.1090/S0002-9947-1993-1132435-7
- MathSciNet review: 1132435