Local Cohomology Based On A Nonclosed Support Defined By A Pair Of Ideals

Local cohomology theory is an indespensibile and significant tool in commutative al-gebra and algebraic geometry. In recent years, there are many mathematicians dedicate to research in this area and get many good conclusions. In 2008, R. Takahashi, Y. Yoshino and T. Yoshizawa promoted the classical local cohomology theory, introduced local cohomology modules based on a nonclosed support defined by a pair of ideals, and found that they have many properties that are similar to the classical local cohomology modules.Based on paper[20], this paper do some further research on the properties of the local cohomology modules defined by a pair of ideals and get some good conclusions. Such as: local cohomology difined by a pair of ideals communicates with localization. The second part of this paper is focus on discussing when the extension funtors of a local cohomology module are weakly Laskerian. And this paper also dicusses when module HI,Jt(M) is (I, J)-weakly cofinite.