Acyclicity over local rings with radical cube zero

Details Acyclicity over local rings with radical cube zero Acyclicity over local rings with radical cube zero

2006-05-22

arxiv.org/abs/math/0605574v2

Mathematics

Commutative Algebra

Final version, to appear in Illinois J. Math., 15 pp

Scientific paper

This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring $(R,m)$ with $m^3=0$. Conclusive results are obtained on the growth of the ranks of the modules in acyclic complexes, and new sufficient conditions are given for total acyclicity. Results are also obtained on the structure of rings that admit acyclic complexes; part of this structure is exhibited by every ring $R$ that admits a non-free finitely generated non-zero module $M$ with $Ext^n(M,R)=0$ for a few $n>0$.

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