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.
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/6228