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Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
Explores the relationships between tangent spaces, dimensions, and sub-varieties in algebraic geometry.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
Explores the dimension of algebraic varieties, including the (Krull)-dimension of rings and computing dimensions using tools from commutative algebra.
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
