Semistable reduction and local Galois representation for curves

Abstract:
Let $K$ be a $p$-adic number field and $X$ a smooth projective curve over $K$. We consider the first etale cohomology group of $X$ as an l-adic Galois representation $\rho$. In my talk I will report on recent attemps to develop practical algorithms for computing $\rho$ explicitly. These rely on being able to explicitly compute the semistable reduction of $X$.