On the finite generation of a family of Ext modules

2008/09/11 by Tony J. Puthenpurakal, Puthenpurakal, Tony J.
Mathematics · #13A15 (Secondary) #13D07 (Primary) 13A02 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #msc:13A02 #msc:13A15 #msc:13D07 #msc:13H10

paper · pdf · doi:10.48550/arxiv.0809.2068

arxiv created 2008/09/11 · arxiv updated 2009/12/01

Abstract

Let Q be a Noetherian ring with finite Krull dimension and let f= f₁,... f_c be a regular sequence in Q. Set A = Q/(f). Let I be an ideal in A, and let M be a finitely generated A-module with \projdim_Q M finite. Set \R = \bigoplus_{n≥ 0}Iⁿ, the Rees-Algebra of I. Let N = \bigoplus_{j ≥ 0}N_j be a finitely generated graded \R-module. We show that \bigoplus_{j≥ 0}\bigoplus_{i≥ 0} \Extⁱ_A(M,N_j) is a finitely generated bi-graded module over \Sc = \R[t₁,...,t_c]. We give two applications of this result to local complete intersection rings.

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