Drinfeld shtukas on curves over finite fields played a crucial role in the
proof of the Langlands correspondence over global function fields. Although we do not know the definition of shtukas over Spec(Z), there is a category analogous to the category of isoshtukas (i.e., generic fibers of shtukas). The construction of this category is based on the work of Kottwitz on B(F, G) and the idea of Scholze to consider the representations of Kottwitz gerbes over global fields. I will explain the construction of the latter, the aforementioned analogy and the conjectural existence of a Weil cohomology theory taking values in Rep(Kt_Q). If time permits, I will also formulate a couple of related open questions.
