Department Mathematik



Yorck Sommerhäuser


Algebraic Number Theory II

  • Summer semester 2004
  • Lecturer: Y. Sommerhäuser
  • Time: Wednesday, 9:15 am
  • Room: 251
  • Contents: Having discussed the ideal-theoretic approach to algebraic number theory in the first part, we discuss in the second part the valuation-theoretic approach. To connect these two approaches, we assign to every prime ideal a valuation of the algebraic number field. By completion with respect to this valuation, we get new fields, whose properties we will
    Also the second part of the course will be based on the book by J. Neukirch cited below. The first part is currently being videotaped at the "Institut für Unterrichtsmitschau"; the first lectures are already available on streaming video.
  • References:
    • S. Borewicz/I. Safarevic: Zahlentheorie, Birkhäuser, Basel, 1966
    • A. Fröhlich/M. J. Taylor: Algebraic Number Theory, Camb. Stud. Adv. Math. Vol. 27, Cambridge, 1991
    • H. Hasse: Zahlentheorie, Akademie-Verlag, Berlin, 1969
    • H. Koch: Zahlentheorie, Vieweg, Braunschweig, 1997
    • S. Lang: Algebraic Number Theory, Grad. Texts Math., Bd. 110, Springer, Berlin, 1994
    • W. Narciewicz: Elementary and Analytic Theory of Algebraic Numbers, 2. Aufl., Springer, Berlin, 1990
    • J. Neukirch: Algebraische Zahlentheorie, Springer, Berlin, 1992