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Academic Year 2023/2024 - Teacher: ALESSIO MOSCARIELLO

Required Prerequisites

Knowledge of basic concepts in commutative algebra and field theory; in particular it is useful to know integral ring extensions and algebraic field extensions.

Detailed Course Content

Recap on integral ring extensions.

Norms, traces and discriminants.

Quadratic and cyclotomic extensions.

Dedekind domains.

Factorization of prime ideals in extensions.

The ideal class group.

The Dirichlet unit theorem.

If there will be time other extra contents (e.g. factorization of prime ideals in Galois extensions) will be added.