Adjunctions and Applications

Related lectures (31)

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Covers the study of graded modules and quasicoherent sheaves in algebraic geometry.

Explores primary decomposition, recovering rings from spectra, and studying regular functions on spectra.

Covers the definition of coherent sheaves and their properties in the context of algebraic geometry.

Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.

Explores tangent spaces in algebraic geometry, defining them as finite-dimensional subspaces of derivations on varieties.

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

Covers regular and smooth projective varieties, hypersurfaces, and algebraic dimensions.

Explores the Albanese morphism of varieties with Kodaira dimension zero in positive characteristic.

Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.

Covers vector bundles, locally free sheaves, depth, Serre twisting sheaf, and graded modules in algebraic geometry.