滤环上微局部化模的正则奇点

Microlocalizations of Modules with Regular Singularities over Filtered Rings

滤环Ｒ上的模在微局部化下的性质是许多文献讨论的问题．Ｅｓｓｅｎ证明了Ｚａｒｉｓｋｉ滤环Ｒ上的模Ｍ若具有正则奇点，则它的微局部化ＱμＳ（Ｍ）作为ＱμＳ（Ｒ）－模仍具有正则奇点，但ＱμＳ（Ｍ）作为Ｒ－模是否仍具有正则奇点则不知道．对这一问题进行了讨论，并证明了若Ｍ是有正则奇点的Ｒ－模且Ｍ上的局部滤是良滤，则ＱμＳ（Ｍ）作为Ｒ－模是具正则奇点的模．在一定条件下解决了该问题．

The microlocalized properties of a module over a filtered ring R are discussed by many papers in recent years.For example,Essen proved that if M is a module with regular singularities over a Zariski ring R ,then its microlocalization Q μ S(M) is a Q μ S(R) module with regular singularities.But it is unknown that if Q μ S(M) is a R module with regular singularities.In this paper the regular singularities of the microlocalization Q μ S(M) are discussed as an R module while R is a Zariski filtered ring and M is an R module with regular singularities.An answer to the problem in suitable conditions is given.The result is proved that if M is a R module with regular singularities and the localized filtation on M is a good R filtration then the microlocalization Q μ S(M) of M is a R module with regular singularities.