Samuele Anni (Heidelberg)

15 Dec 2016 - W01 0-012 (Wechloy), 4 pm s.t.

The inverse Galois problem and hyperelliptic curves

The inverse Galois problem is one of the greatest open problems in group theory and also one of the easiest to state: is every finite group a Galois group? Hilbert was the first to study it in earnest: Hilbert's irreducibility theorem established a connection between Galois groups over Q and Galois groups over Q[x], and this led him to show that symmetric and alternating groups are realisable over Q as Galois groups.
My interest around this problem is connected to the realization of linear and symplectic groups as Galois groups over Q and over number fields.
In this talk I will give examples of uniform realisations using elliptic curves and genus 2 curves. After this introduction, I will explain how to extend these results for higher genus using Jacobians of hyperelliptic curves (work in progress with Vladimir Dokchitser).