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Transactions of the American Mathematical Society

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Extensions of modules over Weyl algebras


Author: S. C. Coutinho
Journal: Trans. Amer. Math. Soc. 349 (1997), 3343-3352
MSC (1991): Primary 16S32; Secondary 16E30, 13N10
DOI: https://doi.org/10.1090/S0002-9947-97-01901-6
MathSciNet review: 1407699
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Abstract: In this paper we calculate some $\mathrm {Ext}$ groups of singular modules over the complex Weyl algebra $A_{n}$. In particular we determine conditions under which $\mathrm {Ext}$ is an infinite dimensional vector space when $n =2$ or $3$.


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  • 1. I.N. Bernstein and V. Lunts, On non-holonomic irreducible $D$-modules, Invent. Math. 94 (1988), 223-243. MR 90b:58247
  • 2. J.-E. Björk, Rings of differential operators, North-Holland Publishing Company, Amsterdam, 1979. MR 82g:32013
  • 3. J.-E. Björk, Filtered noetherian rings, Noetherian Rings and Their Applications (L.W. Small, ed.), Mathematical Surveys and Monographs 24, American Mathematical Society, Providence, 1987. MR 89c:16018
  • 4. S.C. Coutinho, Modules of codimension one over Weyl algebras, J. Algebra 177 (1995), 102-114. MR 96i:16041
  • 5. S.C. Coutinho, Krull dimension of modules and involutive ideals, Proc. Amer. Math. Soc. 123 (1995), 1647-1654. MR 95g:16023
  • 6. O. Gabber, The integrability of the characteristic variety, Amer. J. Math. 103 (1981), 445-468. MR 82j:58104
  • 7. V. Ginsburg, Characteristic varieties and vanishing cycles, Invent. Math. 84 (1986), 327-402. MR 87j:32030
  • 8. A. Gyoja, Theory of pre-homogeneous vector spaces without regularity condition, Publ. RIMS, Kyoto Univ. 27 (1991), 861-922. MR 93f:22018
  • 9. R. Hartshorne, Algebraic geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York-Heidelberg-Berlin, 1977. MR 57:3116
  • 10. M. Kashiwara, $B$-functions and holonomic systems: rationality of roots of $B$-functions, Invent. Math. 47 (1976), 33-53. MR 55:3309
  • 11. T. Levasseur, Equidimensionalité de la variété caractéristique, exposé de O. Gabber rédigé par T. Levasseur, unpublished.
  • 12. V. Lunts, Algebraic varieties preserved by generic flows, Duke Math. J. 58 (1989), 531-554. MR 91a:32015
  • 13. J. C. McConnell and J. C. Robson, Noncommutative noetherian rings, John Wiley and Sons, New York, 1987. MR 89j:16023
  • 14. G. Perets, $d$-critical modules of length $2$ over Weyl algebras, Israel J. Math. 83 (1993), 361-368. MR 94m:17007

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Additional Information

S. C. Coutinho
Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box 68530, 21945-970, Rio de Janeiro, RJ, Brazil
Email: collier@impa.br

DOI: https://doi.org/10.1090/S0002-9947-97-01901-6
Keywords: Weyl algebra, ${\mathcal{D}}$-module, characteristic variety, $\mathrm{Ext}$-groups
Received by editor(s): February 22, 1996
Article copyright: © Copyright 1997 American Mathematical Society

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