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Eisenbud, David

Homological algebra of a complete intersection, with an application to group representations. (English) Zbl 0444.13006

Trans. Am. Math. Soc. 260, 35-64 (1980).
Author’s abstract: Let \(R\) be a regular local ring, and let \( A=R/(x)\), where \(x\) is any nonunit of \(R\). We prove that every minimal free resolution of a finitely generated \(A\)-module becomes periodic of period 1 or 2 after at most \(\dim A\) steps, and we examine generalizations and extensions of this for complete intersections. Our theorems follow from the properties of certain universally defined endomorphisms of complexes over such rings.
Reviewer: David Eisenbud
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Cited in 24 Reviews
Cited in 322 Documents

MSC:

13D99 Homological methods in commutative ring theory
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
14M10 Complete intersections
13D25 Complexes (MSC2000)
13H05 Regular local rings

Keywords:

complete intersection; periodicity of minimal free resolution; regular local ring; matrix factorization
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\textit{D. Eisenbud}, Trans. Am. Math. Soc. 260, 35--64 (1980; Zbl 0444.13006)
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References:

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