Let X be a smooth proper variety over a p-adic field with good reduction. Thanks to a theorem of Faltings, the etale cohomology of X with certain coefficients called crystalline local systems can be related to crystalline cohomology groups of a reduction of X. In my talk, I will review this connection and some of the necessary background. Then I will present a different description of integral crystalline local systems, extending a recent result of Bhatt-Scholze to higher dimensions. Joint work with Haoyang Guo. Speaker(s): Emanuel Reinecke (MPIM Bonn)