Wild Galois representations of hyperelliptic curves.

In this talk we will investigate the Galois action on the Tate module of a certain family of hyperelliptic curves defined over local fields. In particular we will look at curves with potentially good reduction, which acquire good reduction over a wildly ramified "large" extension. We will first introduce the definition of l-adic Galois representation attached to a hyperelliptic curve, then we will clarify what we mean by "large" and finally show how to determine the Galois representation in the case considered.