Teachers: Qing Liu and Pascal Autissier
Program:
- valued fields : absolute values, valuations, complete valued fields, normed vector spaces, extensions of absolute values, Hensel’s lemma.
- ramification : unramified extensions, totally ramified extensions, tame and wild ramification.
- local fields : structure of their valuation rings, Witt vectors.
Prerequisites:
- Theory of Galois extensions of fields;
- Basic notion of commutative algebra (modules, localization).
Bibliography:
P. Samuel: Théorie algébrique des nombres, Hermann, Paris, 1967
J. Neukirch: Algebraic number theory, GMW 322, Springer, 1999
Z. Borevich, I. Shafarevich: Number theory, Academic Press 1966
J.W.S. Cassels, A. Fröhlich (eds): Algebraic number theory, Aca