Special Year Seminar

The notion of $p$-adic shtukas are introduced by Scholze in his Berkeley lectures on $p$-adic geometry. They are closely related to $p$-divisible groups when their ``legs" are bounded by some minuscule cocharacter. But compared to $p$-divisible groups, their moduli stacks have better geometric properties. Furthermore, these moduli stacks (should) control the integral structure of Shimura varieties at the prime $p$, in the sense of a cartesian diagram conjectured by Scholze. I will explain these ideas, partly based on an ongoing joint work with Daniels, van Hoften and Kim.