TY - JOUR
T1 - Finiteness properties of local cohomology modules
T2 - A characteristic-free approach
AU - Lyubeznik, Gennady
N1 - Funding Information:
Supported by the National Science Foundation.
PY - 2000/7/17
Y1 - 2000/7/17
N2 - If R is a commutative Noetherian regular ring containing a field and I is an ideal of R, it is known that every local cohomology module of R with support in I has finite Bass numbers and a finite set of associated primes. However, the previously available proofs of this result were completely different from each other in characteristic p > 0 and in characteristic 0. The purpose of this paper is to give a characteristic-free proof of this result modulo a result from the theory of D-modules which has a completely characteristic-free statement but for which we do not know a characteristic-free proof.
AB - If R is a commutative Noetherian regular ring containing a field and I is an ideal of R, it is known that every local cohomology module of R with support in I has finite Bass numbers and a finite set of associated primes. However, the previously available proofs of this result were completely different from each other in characteristic p > 0 and in characteristic 0. The purpose of this paper is to give a characteristic-free proof of this result modulo a result from the theory of D-modules which has a completely characteristic-free statement but for which we do not know a characteristic-free proof.
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U2 - 10.1016/S0022-4049(99)00080-8
DO - 10.1016/S0022-4049(99)00080-8
M3 - Article
AN - SCOPUS:0034679343
SN - 0022-4049
VL - 151
SP - 43
EP - 50
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1
ER -