Vol. 282, No. 1, 2016

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Associated primes of local cohomology modules over regular rings

Tony J. Puthenpurakal

Vol. 282 (2016), No. 1, 233–255

Let R be an excellent regular ring of dimension d containing a field K of characteristic zero. Let I be an ideal in R. We show that AssHId1(R) is a finite set. As an application, we show that if I is an ideal of height g with heightQ = g for all minimal primes of I then for all but finitely many primes P I with heightP g + 2, the topological space Spec(RPIRP) is connected. We also show that to prove a conjecture of Lyubeznik (regarding finiteness of associate primes for local cohomology modules) for all excellent regular rings of dimension d containing a field of characteristic zero, it suffices to prove AssSHJg+1(S) is finite for all ideals J in S of height g (here 0 g d), where S is an excellent regular domain of dimension d containing an uncountable field of characteristic zero.

local cohomology, associate primes, $D$-modules
Mathematical Subject Classification 2010
Primary: 13D45
Secondary: 13D02, 13H10
Received: 10 June 2015
Revised: 20 August 2015
Accepted: 22 August 2015
Published: 24 February 2016
Tony J. Puthenpurakal
Department of Mathematics
Indian Institute of Technology Bombay
Mumbai 400 076