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Volume 24 Issue 1
Jan.  1998
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Journal of Beijing University of Aeronautics and Astronautics  > 1998  >  24(1): 100-103.
Zhou Meng. Microlocalizations of Modules with Regular Singularities over Filtered Rings[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(1): 100-103. (in Chinese)
Citation: Zhou Meng. Microlocalizations of Modules with Regular Singularities over Filtered Rings[J]. Journal of Beijing University of Aeronautics and Astronautics, 1998, 24(1): 100-103. (in Chinese)
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Microlocalizations of Modules with Regular Singularities over Filtered Rings

  • Beijing University of Aeronautics and Astronautics,Dept.of Applied Mathematics and Physics

  • Received Date: 05 Jun 1996
  • Publish Date: 31 Jan 1998
    Abstract
  • 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.

     

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    • References(1)
  • 1. Essen A V D.Modules with regular singularities over filtered rings and algebraic microlocalization.Lecture Notes in Mathematics 1296,New York:Springer Verlag,1987.384~398 2. Essen A V D.Modules with regular singularities over filtered rings.Publ RIMS Kyoto Univ,1986,22:849~887 3. Nastasescu C,Van Oystaeyen F.Graded ring theory (Math Lib 28).Amsterdam:North Holland,1982 4. Nastasescu C,Van Oystaeyen F.Topics in the theory of graded and filtered rings and modules.Lecture Notes in Mathematics 758,New York:Springer Verlag,1978.259~271 5. Bjork J E.Rings of differential operators (Math Lib 21).Amsterdam:North Holland,1979 6. Bjork J E.The Auslader condition on Noetherian rings.Lecture Notes in Mathematics 1404,New York:Springer Verlag,1989.137~173 7. Asensio M J,Van Bergh M,Van Oystaeyen F.A new algebraic approach to microlocalization of filtered rings.Trans A M S,1989,316(2):537~553
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