Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Sara Arias-de-Reyna
Affiliation:

HIM, Bonn
Date:

Wed, 14/04/2010 - 14:15 - 15:15 In this talk we address the following strengthening of the Inverse Galois problem over $\mathbb{Q}$, introduced by B. Birch around 1994: Let $G$ be a finite group. Is there a tamely ramified Galois extension of $\mathbb{Q}$ with Galois group $G$? When $G$ is a linear group, this problem can be approached through the study of Galois representations attached to arithmetic-geometric objects. Let $\ell$ be a prime number. We will consider the Galois representations attached to the $\ell$-torsion points of elliptic curves and abelian surfaces to give an explicit construction of tame Galois realizations of $GL(2, \ell)$ and $GSp(4,\ell)$.

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246