Rigidity of p-adic local systems

Let X be a smooth connected rigid analytic variety over a p-adic field. In this talk we will show that the p-adic etale local systems over X are very rigid in the sense that for any $Z_p$-local system over X,  if it is de Rham at a closed point, then it is a de Rham over X. We will also discussion some applications to Shimura varieties. Joint work with Xinwen Zhu.