Asymptotic depth of Ext modules over complete intersection rings

2018/02/05 by Provanjan Mallick, Tony J. Puthenpurakal, Mallick, Provanjan +1
Mathematics · #13C15. 13C40 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13C15. #msc:13C40

paper · pdf · doi:10.48550/arxiv.1802.01283

arxiv created 2018/02/05 · arxiv updated 2018/02/06

Abstract

Let (A,\mathfrakm) be a local complete intersection ring and let I be an ideal in A. Let M, N be finitely generated A-modules. Then for l = 0,1, the values depth Ext^2i+l_A(M, N/IⁿN) become independent of i, n for i,n ≫ 0. We also show that if \mathfrakp is a prime ideal in A then the j^th Bass numbers μ_j(\mathfrakp, Ext^2i+l_A(M,N/IⁿN)) has polynomial growth in (n,i) with rational coefficients for all sufficiently large (n,i).

Related

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