Number Theory (2024-25)

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