2006/05/22 by Lars Winther Christensen, Christensen, Lars Winther, Oana Veliche +1 · 1 citation
Mathematics · #13D02 #13D25 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13D02 #msc:13D25
paper · pdf · doi:10.48550/arxiv.math/0605574
Final version, to appear in Illinois J. Math., 15 pp
arxiv created 2006/11/23 · arxiv updated 2009/12/01
This paper studies infinite acyclic complexes of finitely generated free modules over a commutative noetherian local ring (R,m) with m3=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 Extn(M,R)=0 for a few n>0.