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Galois representations and the Tame Inverse Galois problem

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Sara Arias-de-Reyna
HIM, Bonn
Wed, 14/04/2010 - 14:15 - 15:15
MPIM Lecture Hall
Parent event: 
Number theory lunch seminar

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 $GSp(4,\ell)$.

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