Asymmetric complete resolutions and vanishing of Ext over Gorenstein rings

2005/10/28 by David A. Jorgensen, Jorgensen, David A., Liana M. Sega +1
Mathematics · #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.math/0510644

14 pages, to appear in Internat. Math. Res. Notices

arxiv created 2005/10/28 · arxiv updated 2009/12/01

Abstract

We construct a class of Gorenstein local rings R which admit minimal complete R-free resolutions \bd C such that the sequence \\rank_R C_i\ is constant for i< 0, and grows exponentially for all i>0. Over these rings we show that there exist finitely generated R-modules M and N such that \Extⁱ_R(M,N)=0 for all i> 0, but \Extⁱ_R(N,M)≠ 0 for all i>0.

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