Étale Motives and the Hodge Conjecture

Explores algebraic cycles, etale cohomology, and counterexamples to the Hodge conjecture.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.