Cofiniteness and vanishing of local cohomology modules
C Huneke, J Koh - Mathematical Proceedings of the Cambridge …, 1991 - cambridge.org
Let R be a noetherian local ring with maximal ideal m and residue field k. If M is a finitely
generated R-module then the local cohomology modules are known to be Artinian.
Grothendieck [3], exposé 13, 1· 2 made the following conjecture: If I is an ideal of R and M is
a finitely generated R-module, then HomR (R/I,) is finitely generated.
generated R-module then the local cohomology modules are known to be Artinian.
Grothendieck [3], exposé 13, 1· 2 made the following conjecture: If I is an ideal of R and M is
a finitely generated R-module, then HomR (R/I,) is finitely generated.
Cofiniteness and vanishing of local cohomology modules, and colength of conductor ideals
D Delfino - 1994 - search.proquest.com
In Chapter 1 we prove a special case of a conjecture by Huneke and Lyubeznik about the
vanishing of local cohomology modules. In Chapter 2 we prove that, if M is a module over a
complete noetherian local ring R and if I is an ideal, then $ H\sbsp {I}{j}(M) $ is I-cofinite if R
is either equicharacteristic, or Cohen-Macaulay, or if the uniformizing parameter of a
coefficeint ring of R is in $\sqrt {I} $. In Chapter 3 we give equivalent conditions for a one-
dimensional local, reduced, excellent ring R to be such that $ t\lambda (R/{\cal C})-\lambda …
vanishing of local cohomology modules. In Chapter 2 we prove that, if M is a module over a
complete noetherian local ring R and if I is an ideal, then $ H\sbsp {I}{j}(M) $ is I-cofinite if R
is either equicharacteristic, or Cohen-Macaulay, or if the uniformizing parameter of a
coefficeint ring of R is in $\sqrt {I} $. In Chapter 3 we give equivalent conditions for a one-
dimensional local, reduced, excellent ring R to be such that $ t\lambda (R/{\cal C})-\lambda …