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 (in preparation)
2. D-modules, flat connections and local systems (in preparation)
3. Good filtrations and the characteristic variety (in preparation)
4. The Bernstein filtration and holonomic modules over the Weyl algebra
5. Bernstein-Sato polynomials
6. Holonomic D-modules and duality (in preparation)
7. Inverse images (in preparation)
8. Direct images and the relative de Rham complex (in preparation)
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 (in preparation)
13. Regular singularities
14. The Riemann-Hilbert correspondence (in preparation)
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.