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Éléments de la théorie des systèmes différentiels géométriques: Cours du C.I.M.P.A. École d'été de Séville (1996)
Edited by: Philippe Maisonobe, Université de Nice, France, and Luis Narváez Macarro, Universidad de Sevilla, Spain
A publication of the Société Mathématique de France.
Séminaires et Congrès
2004; 430 pp; softcover
Number: 8
ISBN-10: 2-85629-151-1
ISBN-13: 978-2-85629-151-1
List Price: US$104
Member Price: US$83.20
Order Code: SECO/8
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The theory of geometric differential systems consists of the study of coherent modules on the ring of differential operators on a complex analytic or algebraic manifold. It is used in various branches of mathematics: algebraic geometry, arithmetics, Lie groups and Lie algebras, algebraic topology of singularities, etc. This book contains articles from lectures given at the Centre International de Mathématiques Pures et Appliquées (C.I.M.P.A.) summer school. It offers a complete survey of the theory, taking into account the most recent advances.

The volume is suitable for graduate students and researchers interested in algebra and algebraic geometry.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and researchers interested in algebra and algebraic geometry.

Table of Contents

  • Ph. Maisonobe and T. Torrelli -- Image inverse en théorie des \(\mathcal{D}\)-modules
  • L. N. Macarro -- The local duality theorem in \(\mathcal{D}\)-module theory
  • F. J. Castro-Jiménez and M. Granger -- Explicit calculations in rings of differential operators
  • L. N. Macarro and A. R. León -- Continuous division of linear differential operators and faithful flatness of \(\mathcal{D}_X^\infty\)over \(\mathcal{D}_X\)
  • J. Briançon -- Extensions de Deligne pour les croisements normaux
  • Z. Mebkhout -- Le théorème de positivité, le théorème de comparaison et le théorème d'existence de Riemann
  • Ph. Maisonobe and Z. Mebkhout -- Le théorème de comparaison pour les cycles évanescents
  • B. Malgrange -- On irregular holonomic \(\mathcal{D}\)-modules
  • Y. Laurent -- Geometric irregularity and \(\mathcal{D}\)-modules
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