Lectures related to Grothendieck category

Explores the complement problem for hypersurfaces in projective spaces and discusses isomorphism based on their complements.

Covers the Weil conjectures on rationality, functional equation, and the Riemann hypothesis, exploring properties of varieties in algebraic geometry.

Introduces adjunctions in category theory, exploring necessary conditions and natural transformations for adjoint functors.

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.