滤环上微局部化模的正则奇点

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Q\+μ\-S(M)作为Q\+μ\-S(R) 模仍具有正则奇点,但Q\+μ\-S(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Q\+μ\-S(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. 

Microlocalizations of Modules with Regular Singularities over Filtered Rings

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.