Étale Motives and the Hodge Conjecture

Related lectures (30)

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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.

Presents a proof that smooth projective varieties with nef anti-canonical divisor have surjective Albanese morphism.

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores Lie groups, scalar fields, and vector spaces transformations.