Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-28T16:19:36.105Z Has data issue: false hasContentIssue false
  • English
  • Français

On the comparison theorem for elementary irregular D-modules

Published online by Cambridge University Press:  22 January 2016

Claude Sabbah
Claude Sabbah*
Affiliation:
URA 169 du C.N.R.S. Centre de Mathématiques Ecole Polytechnique, F-91128 Palaiseau cedex, France e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let U be a smooth quasi-projective variety over C and let f be a regular function on U. Let DU be the sheaf of algebraic differential operators on U and let M be a regular holonomic DU-module: here, regular means that there exists some smooth compactification X of U and some extension of M as a DX-module which is regular holonomic on X (one also may avoid the use of a smooth compactification to define regularity, see [17]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 141 , March 1996 , pp. 107 - 124
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1996

References

[ 1 ] Aomoto, K., Kita, M., Orlik, P., Terao, H., Twisted de Rham cohomology groups of logarithmic forms, preprint (1994) to appear in Adv. in Math.Google Scholar
[ 2 ] Borel, A., et al., Algebraic D-modules, Perspectives in Math. vol. 2, Academic Press, Boston, 1987.Google Scholar
[ 3 ] Borel, A., Algebraic D-modules, Chapters VI to IX in [2], 207–352.Google Scholar
[ 4 ] Briançon, J., Maisonobe, Ph., Sur la variété caractéristique de systèmes différentiels irréguliers le long d’une hypersurface, C. R. Acad. Sci. Paris 320 (1995), 285–288.Google Scholar
[ 5 ] Broughton, S. A., Milnor numbers and the topology of polynomial hypersurfaces, Invent. Math., 97 (1988), 217–241.CrossRefGoogle Scholar
[ 6 ] Brylinski, J. L., (Co)homologie d’intersection et faisceaux pervers, in Séminaire Bourbaki, Astérisque, 92–93 (1982), 129–157.Google Scholar
[ 7 ] Brylinski, J. L., Transformations canoniques, dualité projective, in Géométrie et analyse microlocales, Astérisque, 140–141 (1986), 3–134.Google Scholar
[ 8 ] Dimca, A., Saito, M., On the cohomology of the general fiber of a polynomial map, Compositio Math., 85 (1993), 299–309.Google Scholar
[ 9 ] Kashiwara, M., On the maximally overdetermined systems of differential equations, Publ. R.I.M.S. Kyoto Univ., 10 (1975), 563–579.CrossRefGoogle Scholar
[10] Kashiwara, M., Schapira, P., Sheaves on Manifolds, Grundlehren der mathematischen Wissenschaften 292, Springer-Verlag, Berlin, Heidelberg, 1990.Google Scholar
[11] Kohno, T., Homology of a local system on the complement of hyperplanes, Proc. Japan Acad., 62 (1986), 144–147.Google Scholar
[12] Lê, D. T., Le concept de singularité isolée de fonction analytique, Advanced Studies in Pure Math., 8 (1986), 215–227.Google Scholar
[13] Loeser, F., Sabbah, C., Equations aux différences finies et déterminants d’intégrales de fonctions multiformes, Comment. Math. Helv., 66 (1991), 458–503.Google Scholar
[14] Malgrange, B., Equations différentielles à coefficients polynomiaux, Progress in Math. vol. 96, Birkhaüser, Boston, 1991.Google Scholar
[15] Malgrange, B., letter to P. Deligne, April 30, 1991.Google Scholar
[16] Mebkhout, Z., Le formalisme des six opérations de Grothendieck pour les D-modules cohérents, Hermann, Paris, 1989.Google Scholar
[17] Mebkhout, Z., Le théorème de comparaison entre cohomologies de de Rham d’une variété algébrique complexe et le théorème d’existence de Riemann, Publ. Math. I.H.E.S., 69 (1989), 47–89.Google Scholar
[18] Mebkhout, Z., Le théorème de positivité de l’irrégularité pour les DX -modules, in The Grothendieck Festschrift vol. III, Progress in Math., Birkhaüser, Boston, 88 (1990), 83–132.Google Scholar
[19] Mebkhout, Z., Narváez-Macarro, L., Démonstration géométrique du théorème de constructibilité, pages 248 to 253 in [16].Google Scholar
[20] Mebkhout, Z., Narváez-Macarro, L., Le théorème de constructiblilité de Kashiwara, in Eléments de la théorie des systèmes différentiels vol. 2, Hermann, Paris (1993), 47–98.Google Scholar
[21] Mebkhout, Z., Sabbah, C., D-modules et cycles évanescents, chapter III § 4 in [16].Google Scholar
[22] Saito, M., letter to A. Dimca, April 30, 1991.Google Scholar
[23] Kashiwara, M., Schapira, P., Microlocal study of sheaves, Astérisque, 128 (1985).Google Scholar