Abstract:
We will define the pro-étale site of a  scheme after Bhatt and Scholze, which is an enlargement of the classical étale site and discuss some of its properties. Using this formalism we will define  categories  of pro-étale  (lisse) adic sheaves and compare them to the classical ones defined by Deligne. Furthermore we define the derived category of constructible pro-étale adic sheaves and relate it to Ekedahl's adic formalism.