Algebraic de Rham cohomology

Welcome! My name is Dustin Clausen and I'm a mathematician at the University of Copenhagen. This is the website for a class I'm teaching on algebraic de Rham cohomology.

Lecture 1: de Rham cohomology of real manifolds

Lecture 2: Interlude on D(R)

Lecture 3: Interlude on sheaves with values in D(Z)

Lecture 4: de Rham cohomology of complex manifolds

Lecture 5: Grothendieck's theorem, part 1

Lecture 6: Grothendieck's theorem, part 2

Lecture 7: Kahler differentials, smooth maps, and the de Rham complex

Lecture 8: Derived quasi-coherent sheaves

Lecture 9: Globalization and Deligne's theorem on degeneration

Lecture 10: Deligne's theorem, part 2

Lecture 11: de Rham cohomology in characteristic p: pathological?

Lecture 12: Equivariant de Rham cohomology: set-up and definition

Lecture 13: Totaro's theorem on Hodge cohomology of classifying stacks

Lecture 14: Chern classes and Thom classes

Lecture 15: Cycle classes and deformation to the normal bundle

Lecture 16: Poincare duality