How to calculate the slopes of a D -module

A. Assi; F. J. Castro-Jiménez; J. M. Granger

Compositio Mathematica (1996)

  • Volume: 104, Issue: 2, page 107-123
  • ISSN: 0010-437X

How to cite


Assi, A., Castro-Jiménez, F. J., and Granger, J. M.. "How to calculate the slopes of a $D$-module." Compositio Mathematica 104.2 (1996): 107-123. <>.

author = {Assi, A., Castro-Jiménez, F. J., Granger, J. M.},
journal = {Compositio Mathematica},
keywords = {critical index; slope of a coherent -module; Newton polygon},
language = {eng},
number = {2},
pages = {107-123},
publisher = {Kluwer Academic Publishers},
title = {How to calculate the slopes of a $D$-module},
url = {},
volume = {104},
year = {1996},

AU - Assi, A.
AU - Castro-Jiménez, F. J.
AU - Granger, J. M.
TI - How to calculate the slopes of a $D$-module
JO - Compositio Mathematica
PY - 1996
PB - Kluwer Academic Publishers
VL - 104
IS - 2
SP - 107
EP - 123
LA - eng
KW - critical index; slope of a coherent -module; Newton polygon
UR -
ER -


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  2. 2 Buchberger, B.: Ein algorithmisches Kriterium for die Lösbarkeit eines algebraischenGleichungssystems Aequationes Math., 4 (1970) 374-383. Zbl0212.06401MR268178
  3. 3 Castro, F.: Thèse de 3ème cycle, Université Paris VII, 1984. 
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  5. 5 Laurent, Y. and Mebkhout, Z.: Le polygone de Newton d'un DX -module, to appear. Zbl0993.35007
  6. 6 Lazard, D.: Gröbner bases, Gaussian elimination and resolution of systems of algebraic equations, Proc. of Eurocal 83, Springer, L.N.C.S. 162, 146-156. Zbl0539.13002MR774807
  7. 7 Lejeune-Jalabert, M. and Teissier, B.: Transversalité, polygone de Newton et installations, in 'Singularités à Cargèse', Astérisque7-8 (1973) 75-119. Zbl0298.14002MR409469
  8. 8 Malgrange, B.: Sur la reduction formelle des équations différentielles à singularités irrégulières, Prépub. Institut Fourier (1979). 
  9. 9 Mebkhout, Z.: Le théorème de positivité de l'irrégularité pour les D-modules, Grothendieck Festschrift III, Progress in Math. 88 (1990) 84-131. Zbl0731.14007
  10. 10 Mebkhout, Z.: Le polygone de Newton d'un DX-module, Proceedings of the third Algebraic Geometry Conference, La Rábida 1991, Progress in Math., 134 (1996) 237-258. Zbl0853.58095MR1395185
  11. 11 Mora, T.: Seven variations on standard bases, Preprint, University of Genova, 1988. 
  12. 12 Ramis, J.P.: Théorème d'indice Gevrey pour les équations différentielles ordinaires, Mem. AMS296 (1984). Zbl0555.47020
  13. 13 Sabbah, C.: Proximité evanescente I. La structure polaire d'un D-module. Appendice en collaboration avec F. Castro, Compositio Math.62 (1987) 283-328. Zbl0622.32012MR901394

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