The p-adic Riemann-Hilbert Correspondence

 

In this talk, I will introduce differential equations on p-adic analytic varieties. We will see how the ultrametric p-adic topology is an obstruction to a Cauchy-Lipschitz-type result. I will then show, following Scholze, how the pro-étale topology and the introduction of new numbers called "periods" provide a workaround to this issue.