An introduction to \(\mathcal{D}\)-modules. (English) Zbl 0816.35004

Schneiders, Jean-Pierre

Bull. Soc. R. Sci. Liège 63, No. 3-4, 223-295 (1994).

This work is based on lectures given at the “Journées d’Analyse Algébrique” held at the University of Liège in March 1993 by the author and is a nice exposition on the algebraic theory of systems of partial differential equations in the complex domain. He performs a detailed study of differential operators and its modules. In particular, he proves its coherence and computes its homological dimension.

Reviewer: J.Kajiwara (Fukuoka)

MSC:

35A27	Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35A10	Cauchy-Kovalevskaya theorems

Keywords:

\({\mathcal D}\)-modules; algebraic theory of systems of partial differential equations in the complex domain; homological dimension