Explores the Riemann zeta function, its properties, applications, and analogies in number theory and algebraic geometry.
Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.
