Abstract：

A classical theorem of Riemann states that complex abelian varieties are classified by their singular homology together with the Hodge filtration. In 2012 Scholze and Weinstein propose a classification of $p$-divisible groups over the $p$-adic complex numbers using analogous linear algebraic data that we may call $p$-adic local shtukas. This development lead to the introduction and study of moduli spaces of $p$-adic local shtukas, which are shown in the Berkeley notes to be generalizations of Rapoport--Zink spaces. In this talk we discuss the v-stack of $p$-adic local and its relation to the moduli problem introduced in the Berkeley notes. We will also discuss two related theorems, the first one explains the relation between the $p$-adic local shtukas and BKF-modules in terms of sheafification. The second one states that stacks of $p$-adic local shtukas are Artin v-stack. The proof of both theorems rely on the theory of kimberlites, we will give an introduction to this theory in the form of a mini-course.