Samuele Anni (Heidelberg)

15.12.2016 - W01 0-012 (Wechloy), 16 Uhr 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 realizable 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 realizations 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 with Vladimir Dokchitser).