Function field of an algebraic variety

Formal sciences
Mathematics
Geometry
Algebraic geometry

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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.

Primary Decomposition: Behaviour and Localisation

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

Projective Plane Curves

Introduces projective plane curves, degrees, components, multiplicities, intersection numbers, tangents, and multiple points, culminating in the statement of Bézout's theorem and its consequences.

Dimension of Algebraic Variety

Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.

Limits and Operations on Limits

Covers limits, algebraic operations, and infinite limits with examples of functions' behavior near limit points.

Terminologie conventions

Covers the terminology and conventions related to the limit of a function and introduces algebraic and transcendental functions.

Error-Correcting Codes: Hamming Distance and Polynomial Multiplication

Covers error-correcting codes, Hamming distance, and polynomial multiplication in algebraic fields.

DVR and Irreducible Plane Curves

Explores Discrete Valuation Rings and their role in irreducible plane curves.

Properties of Finite Dimensional Algebras

Covers the properties of finite dimensional algebras and non-semisimple representations.

Morphisms between Affine Varieties

Covers defining morphisms between affine algebraic varieties and constructing morphisms using algebraic homomorphisms.