Homological algebra on a complete intersection, with an application to group representations

Eisenbud, David

doi:10.1090/S0002-9947-1980-0570778-7

Homological algebra on a complete intersection, with an application to group representations
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by David Eisenbud

Trans. Amer. Math. Soc. 260 (1980), 35-64

DOI: https://doi.org/10.1090/S0002-9947-1980-0570778-7

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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 $\operatorname {dim} A$ 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.

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