Function field of an algebraic variety

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Related lectures (32)

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Continuous Functions and Elementary Functions

Covers the definition and properties of continuous functions on open intervals and elementary functions.

Continuous Functions on Open Intervals

Explores continuous functions on open intervals and elementary functions constructed from algebraic functions.

Affine Algebraic Sets

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

Riemann Zeta Function

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

Projective Space and Algebraic Sets

Introduces projective space and algebraic sets, discussing homogeneous coordinates, ideals, and generators.

Discrete Log Problem: Index Calculus

Explores the discrete log problem and index calculus method in cryptography.

Real Functions of Real Variables: Properties and Domains

Covers the properties of real functions, domains, and types of functions, including periodicity.

Irreducible Algebraic Sets

Explores irreducible algebraic sets and their unique decomposition into components, with a focus on prime ideals and plane subsets classification.

Functions Composition: Continuity & Elements

Covers the composition of functions, continuity, and elementary functions, explaining the concept of continuity and the construction of elementary functions.

Affine Algebraic Varieties: Zariski Topology

Explores affine algebraic varieties, emphasizing the Zariski Topology and regular functions.