On Artinianness of Formal Local Cohomology, Colocalization and Coassociated Primes

Abstract

ABSTRACT. This paper at first concerns some criteria on Artinianness and vanishing of formal local cohomology modules. Then we consider the cosupport and the set of coassociated primes of these modules more precisely.

On top local cohomology modules, Matlis duality and tensor products

“…For the proof of (2), (3), (4) and (7) we refer the reader to [7, 3.3 We recall the ith formal local cohomology of M with respect to a as F i a (M ) := lim ← −n H i m (M/a n M ). See [16] and [5] for more information. It should be noted that Proof.…”

On the relation between formal grade and depth with a view toward vanishing of Lyubeznik numbers

“…[25]). For more information on this topic we refer the reader to [25], [3] and [10]. In the case (R, m)…”

Artinianness and finiteness of formal local cohomology modules with respect to a pair of ideals

“…The same conclusion we have for F i a,I,J (M) when J = 0. These new definitions are a natural generalization of a-formal local cohomology with respect to b and a-formal local cohomology, both introduced by Schenzel [29] and discussed by Mafi [22], Asgharzadeh and Divaaani-Aazar [2], Gu [16], Bijan-Zadeh and Rezaei [3], and Eghbali [11]. However the isomorphism betweenF i a,I,J (M) and F i a,I,J (M) does not happen always, differently as the ordinary formal local cohomology.…”