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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



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

Author: David Eisenbud
Journal: Trans. Amer. Math. Soc. 260 (1980), 35-64
MSC: Primary 13D25; Secondary 13H10, 14M10, 18G10, 20C20
MathSciNet review: 570778
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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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