A NOTE ON ENDOMORPHISMS OF LOCAL COHOMOLOGY MODULES

作者：Mahmood Waqas^*; Zahid Zohaib

来源：Bulletin of the Korean Mathematical Society, 2017, 54(1): 319-329.

DOI：10.4134/BKMS.b160111

• local cohomology
• endomorphism ring
• completion functor
• cohomologically
• complete intersection

Let I denote an ideal of a Noetherian local ring (R, m). Let M denote a finitely generated R-module. We study the endomorphism ring of the local cohomology module H-I(C) (M), c = grade(I, M). In particular there is a natural homomorphism
Hom((R) over capI) ((M) over cap (I), (M) over cap (I)) -> Hom(R)(H-I(C) (M),H-I(C) (M)),
where (center dot) over capI denotes the I -adic completion functor. We provide sufficient conditions such that it becomes an isomorphism. Moreover, we study a homomorphism of two such endomorphism rings of local cohomology modules for two ideals J subset of I with the property grade(I, M) = grade(J, M). Our results extends constructions known in the case of M = R (see e.g. [8], [17], [18]).

• 出版日期2017-1