Universität Regensburg   IMPRESSUM   DATENSCHUTZ
Fakultät für Mathematik Universität Regensburg
Local class field theory with formal modules
Semester
SoSe 2023

Lecturer
Niko Naumann

Type of course (Veranstaltungsart)
Vorlesung

German title
Lokale Klassenkörpertheorie mit formalen Moduln

Contents
Class field theory gives an intrinsic description of all abelian Galois extensions of a given field.
The class field theory of the rationals is encounter very early on: roots of the polynomials X^n-1=0
generate abelian Galois extensions of the rationals, though it is hard to see, that in fact
essentailly all such extensions are obtained. There is no known such description for a general
number field in place of the rationals However, over a complete local field like the p-adic numbers,
the situation is much better: The theory of Lubin-Tate modules provides a way of systematically
producing equations the roots of which generate all abelian extensions.

Literature
see GRIPS

Recommended previous knowledge
basic algebra, including Galois theory. Previous encounter with p-adics is helpful but not strictly
necessary, as we will provide a review of this.

Time/Date
Wed, 4-6 pm H31 and Fri, 10-12 am, H32

Location
excersise class: Fri, 12-2 pm, M101

Course homepage
https://elearning.uni-regensburg.de/course/view.php?id=60081
(Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern)

Registration
  • Registration for course work/examination/ECTS: FlexNow
Course work (Studienleistungen)
  • Successful participation in the exercise classes: Present at least two solutions correctly.
Examination (Prüfungsleistungen)
  • Written exam: Duration: 3 hours, Date: TBD, re-exam: Date: TBD
Modules
BAlg(2), BV, MV, MArGeo, LA-GyAlg

ECTS
9