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Classification of the Tor-algebras of codimension four Gorenstein local rings. (English) Zbl 0565.13004
Let R,m,k be a Gorenstein local ring in which 2 is a unit and assume that k has square roots. Let K be a grade four Gorenstein ideal in R; and Let \(\Lambda_{\bullet}\) be the graded algebra Tor\({}^ R_{\bullet}(R/K,k)\). We prove that \(\Lambda_{\bullet}\) is a Poincaré duality algebra with one of just four possible forms for the multiplication in non-complementary degrees. In subsequent work with C. Jacobsson this result is used to demonstrate rationality of the Poincaré series \(P_{R/K}\). The main technique used is that of tight double linkage, a notion developed by the authors in earlier work, which enables one to understand the minimal free resolution of R/K in great detail.

13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13D03 (Co)homology of commutative rings and algebras (e.g., Hochschild, André-Quillen, cyclic, dihedral, etc.)
18G15 Ext and Tor, generalizations, Künneth formula (category-theoretic aspects)
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