Morphisms and Local Rings

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Regularity and Geometric Meaning

Explores regularity in algebraic geometry and the geometric implications of the Jacobian criterion.

Regular Functions on Quasi-Affine Varieties

Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.

Complex Manifolds: GAGA Principle

Covers the GAGA principle, stating that any morphism on projective varieties is constant.

Redly Constructed Morphisms

Explores the construction and properties of morphisms, focusing on effective divisors, isomorphism of semi-groups, and the relationship between sheaves and factorial spaces.

Primary Decomposition: Behaviour and Localisation

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

Geometric Objects in Algebra

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

Lie Algebras: Introduction and Structure

Introduces Lie algebras, vector spaces with a special bracket operation.

Weil Conjectures: Rationality and Function Equation

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

Field of Rational Functions

Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.

Affine Algebraic Sets

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.