Explores the construction of the field of rational functions on a variety and its connection with local rings and dimensions.
Covers the classification of compact p-adic manifolds using the C.o.V-formula and explores smooth algebraic varieties and Hensel's lemma.
Explores algebraic varieties in linear algebra, focusing on their nature, determinants, irreducibility, prime properties, and geometric representation theory.
Introduces projective, quasi-projective, and algebraic varieties, emphasizing the importance of regular functions in defining morphisms.
