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)

Irreducibility and rational points

Short summary

This course will focus on the geometric aspects of Hilbert's irreducibility theorem and irreducible specializations, namely thin sets of rational points in the sense of Serre and varieties of Hilbert type. It will discuss both some of the basics like the Lang-Weil estimates for rational points over finite fields and weak approximation, interesting applications to number theory and arithmetic geometry, like constructing elliptic curves of high rank, and also recent results on algebraic groups and homogeneous spaces.

Course material

  • Extended abstract of the course [pdf]
  • Exercise sheet 1 [pdf]
  • Some slides for Lecture 1 [pdf]
  • Some slides for Lecture 2 [pdf]

Further information

For further information on this course please contact Arno Fehm.