Ideal topologies, local cohomology and connectedness

Abstract

Let [afr ] be an ideal of a local ring ( R , [mfr ]) and let N be a finitely generated R -module of dimension d : It is shown that H d [afr ] ( N ) ≃ H d [mfr ] ( N )/[sum ] n ∈ℕ 〈[mfr ]〉 (0: H d [mfr ] ( N ) [afr ] n ); where for an Artinian R -module X we put 〈[mfr ]〉 X = ∩ n ∈ℕ [mfr ] n X . As a consequence several vanishing and connectedness results are deduced.