Abstract
A note on the associated primes of local cohomology modules for regular local rings
Highlights
Throughout this note, R denotes a commutative Noetherian ring with identity, I an ideal of R and M a finite R -module
Singh [13] and Katzman [8] gave examples to show that HIi(M ) may have infinitely many associated primes
Lyubeznik [10] showed this result for an unramified regular local ring of mixed characteristic R
Summary
Throughout this note, R denotes a commutative Noetherian ring with identity, I an ideal of R and M a finite R -module. The i -th local cohomology module HIi(M ) is not finitely generated. Huneke and Sharp [7] (in the case of positive characteristic) and Lyubeznik [9] (in characteristic zero) showed that if R is a regular local ring containing a field, HIi(R) has only finitely many associated primes for all ideals I and i ⩾ 0 .
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