Mathematik und Statistik
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Schwerpunkt Reelle Geometrie und Algebra > Jun.-Prof. Dr. Arno Fehm

French-German Summer School
Galois Theory and Number Theory
Konstanz, July 18-24 2015

organized by Lior Bary-Soroker (Tel Aviv University), Pierre Dèbes (Université de Lille), Arno Fehm (Universität Konstanz), Zeev Rudnick (Tel Aviv University)

Number theoretical topics in inverse Galois theory

Short summary

The aim of the course will be to introduce the audience to both inverse Galois theory and some number theoretical topics involved in inverse Galois theory. We will set some recent result of the lecturer as the final goal and will use it as a motivation to discuss the topics that it goes through: the Inverse Galois problems, the geometric approach, Hilbert's irreducibility theorem, the Tchebotarev theorem, the Grunwald problem, the Malle conjecture, some diophantine material on curves: Lang-Weil over finite fields, Heath-Brown-Walkowiak over the rationals, etc.

Course material

  • Extended abstract of the course [pdf]
  • Exercises and problems [pdf]
  • Walkowiak's paper on Hilbert's irreducibility theorem [pdf]
  • Riemann Existence Theorem (link) (link)

Further information

For further information on this course please contact Pierre Dèbes.