Vol. 266, No. 2, 2013

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On the finite generation of a family of Ext modules

Tony J. Puthenpurakal

Vol. 266 (2013), No. 2, 367–389
Abstract

Let (A,m) be a local complete intersection ring. Let M,N be finitely generated A-modules and let I be an ideal in A. We show that

⋃  ⋃
AssExtiA(M, InN )
n≥0i≥0

is a finite set. We also show that there exist i0,n0 such that for all i i0 and n n0 we have

        2i                2i
AssExtA(M, InN ) = AssExtA0(M, In0N),
AssExt2Ai+1(M, InN ) = AssExt2Ai0+1(M, In0N).

We prove analogous results for complete intersection rings which arise in algebraic geometry. We also prove that the complexity, cx(M,InN), is constant for all n 0.

Keywords
local complete intersection, asymptotic associate primes, cohomological operators
Mathematical Subject Classification 2010
Primary: 13D07, 13H10
Secondary: 13A15, 13A02
Milestones
Received: 18 September 2008
Revised: 11 April 2013
Accepted: 11 September 2013
Published: 12 November 2013
Authors
Tony J. Puthenpurakal
Department of Mathematics
Indian Institute of Technology Bombay
Powai
Mumbai 400 076
India