A rigidity result for highest order local cohomology modules

Brodmann, M (2002). A rigidity result for highest order local cohomology modules. Archiv der Mathematik, 79(2):87-92.

Abstract

Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ and let \mathfrak a \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) in terms of the local formal behaviour of \mathfrak a . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢® X contains points which are isolated in n-1(Spec(R/\mathfrak a)).

Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ and let \mathfrak a \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) in terms of the local formal behaviour of \mathfrak a . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢® X contains points which are isolated in n-1(Spec(R/\mathfrak a)).

Citations

2 citations in Web of Science®
3 citations in Scopus®