Oberwolfach Seminar: De Rham and Dolbeault cohomology for D-modules

Date:

May 25th - June 2nd, 2007

Organizers:

Yves André, Paris

Claude Sabbah, Palaiseau

Programme:

Differential equations in the complex domain is a classical subject, if any. They have proved to be an essential tool in algebraic geometry, providing examples of algebraic vector bundles with flat connections. D-module theory is a convenient language to treat them from the point of view of algebraic geometry.
The following items will be treated: flat connections, D-modules, coherence, de Rham cohomology, solutions in the space of distributions, filtrations, characteristic varieties, specialization, Newton polygons, regularity and irregularity, direct images. The courses will start from fundamental results and lead to open questions in the domain. Examples in dimension one will be worked out.

Prerequisites:

Basic knowledge in algebraic geometry.

Literature:

- Y. André, F. Baldassari, De Rham cohomology of differential modules on algebraic varieties, Progress in Mathematics, vol. 189, Birkhäuser Verlag, Basel, 2001.
- Ph. Maisonobe, C. Sabbah (eds), Eléments de la théorie des systèmes différentiels, Les cours du CIMPA, Hermann, Paris, 1993.
- Ph. Maisonobe, L. Narvaez Macarro, Eléments de la théorie des systèmes différentiels géométriques, Séminaires et Congrès vol. 8, SMF, Paris, 2004.

Deadline for applications:

April 1, 2007

The seminars take place at the Mathematisches Forschungsinstitut Oberwolfach. The number of participants is restricted to 24. The Institute covers accommodation and food. Travel expenses cannot be reimbursed. Applications including

• full name and address, including e-mail address
• present position, university
• name of supervisor of Ph.D. thesis
• a short summary of previous work and interest

should be sent as hard copy or by e-mail (.ps or .pdf file) to:

Prof. Dr. Gert-Martin Greuel
Universität Kaiserslautern
Fachbereich Mathematik
Erwin Schrödingerstr.
67663 Kaiserslautern, Germany
.