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Transactions of the American Mathematical Society

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A new algebraic approach to microlocalization of filtered rings

Authors: Maria Jesus Asensio, Michel Van den Bergh and Freddy Van Oystaeyen
Journal: Trans. Amer. Math. Soc. 316 (1989), 537-553
MSC: Primary 16A08; Secondary 32C38, 58G07
MathSciNet review: 958890
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Abstract: Using the construction of the Rees ring associated to a filtered ring we provide a description of the microlocalization of the filtered ring by using only purely algebraic techniques.

The method yields an easy approach towards the study of exactness properties of the microlocalization functor. Every microlocalization at a regular multiplicative Ore set in the associated graded ring can be obtained as the completion of a localization at an Ore set of the filtered ring.

References [Enhancements On Off] (What's this?)

  • [1] M. Awami and F. Van Oystaeyen, On filtered rings with Noetherian associated graded rings, Proc. Ring Theory Meeting (Granada, 1986), Springer-Verlag, Berlin and New York, 1987. MR 959739 (89g:16001)
  • [2] J. E. Björk, Rings of differential operators, Math. Library, vol. 21, North-Holland, Amsterdam, 1979. MR 549189 (82g:32013)
  • [3] -, Unpublished notes, 1985.
  • [4] O. Gabber, On the integrability of the characteristic variety, Amer. J. Math. 103 (1981), 445-468. MR 618321 (82j:58104)
  • [5] R. Hartshorne, Algebraic geometry, Springer-Verlag, Berlin, 1977. MR 0463157 (57:3116)
  • [6] C. Nastasescu and F. Van Oystaeyen, Graded ring theory, Math. Library, vol. 28, North-Holland, Amsterdam, 1980.
  • [7] T. Springer, Micro-localization algébrique, Séminaire d'Algèbre Dubreil-Malliavin, Lecture Notes in Math., Springer-Verlag, Berlin, 1980.
  • [8] A. Van den Essen, Algebraic micro-localization, Comm. Algebra 14 (1986), 971-1000. MR 837269 (87i:16004)
  • [9] Li Huishi and F. Van Oystaeyen, Zariskian filtrations, Comm. Algebra (to appear). MR 1030604 (90m:16004)
  • [10] P. Shapira, Microdifferential systems in the complex domain, Grundlehren der Math. Wiss., no. 269, Springer-Verlag, Berlin, 1985. MR 774228 (87k:58251)

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Article copyright: © Copyright 1989 American Mathematical Society

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