D-modules

Algebraic differential operators and flat connections; characteristic varieties and holonomicity; inverse and direct images, duality and minimal extensions; regular singularities, Riemann–Hilbert, localization, stacks, crystals and Fourier transformation.

1. Differential operators and the Weyl algebra
2. D-modules, flat connections and local systems
3. Good filtrations and the characteristic variety
4. The Bernstein filtration and holonomic modules over the Weyl algebra
5. Bernstein-Sato polynomials
6. Holonomic D-modules and duality
7. Inverse images
8. Direct images and the relative de Rham complex
9. Kashiwara's equivalence and D-modules on singular spaces
10. Adjunctions, base change and the projection formula
11. Preservation of holonomicity and minimal extensions
12. The de Rham functor
13. Regular singularities
14. The Riemann-Hilbert correspondence
15. Equivariant and twisted D-modules
16. Beilinson-Bernstein localization
17. D-modules on stacks, ind-schemes and the de Rham prestack
18. The Fourier transform of D-modules

Original text CC0 1.0 unless the lesson states other terms.