Dedekind Function: Analytic Continuation and Euler Product Formula

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Explores the Localization Theorem in Dedekind rings, isomorphism induced by injection, and ramification in field theory.

Prime ideals and local rings

Covers the concept of prime ideals and local rings, emphasizing their importance.

Dimension of Algebraic Variety

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

Commutative Algebra: Recollections

Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.

Primary Decomposition: Understanding Schemes

Explores primary decomposition and schemes in algebraic geometry, emphasizing the importance of working over non-algebraically closed fields and the concept of fibers of morphisms.

Factorisation in Principal Ideal Domains

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

Irreducible Algebraic Sets

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

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Affine Algebraic Varieties: Zariski Topology

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

Primes in arithmetic progressions (II), and Gamma functions

Explores the existence of primes in arithmetic progressions and the properties of the Euler gamma function.