Index Theorems for D-modules

The Euler-Poincare Index is a classical topological invariant of a compact topological space and this notion can be naturally generalized to the frameworks of sheaves or of D-modules. In this seminar, we will see how to compute the Euler-Poincare index for D-modules using special cohomology classes (characteristic classes), based on the work of Schapira and Schneiders. We will also see how to compute a local version of the Euler-Poincaré Index in the holonomic case. Namely, we will study the needed notions to state the Kashiwara's Index Theorem, which gives a purely geometric way to compute the index of the solutions of an holonomic D-module.