Teachers: Qing Liu and Denis Benois
Program:
- Dedekind domains and valuations, extensions.
- Valued fields. Completion and Hensel’s lemma.
- Ramification theory. Unramified extensions, totally ramified extensions. Tame and wild ramification.
- Galois Theory, ramification subgroups.
- Some applications in algebraic geometry.
Prerequisites:
- Theory of Galois extensions of fields;
- Basic notion of commutative algebra (modules, localization).
Bibliography:
F. Lorenz: Algebra II, Universitext (2008), Springer
J. Neukirch: Algebraic number theory, GMW 322 (1999), Springer
J.-P. Serre: Local fields, GTM 67 (1979), Springer