January 24
Jinhe Ye, University of Notre Dame
A model theoretic adic space
Working in the theory of algebraically closed valued fields, Hrushovski and Loeser used the space $\widehat{V}$ of generically stable types concentrating on $V$ to study the topology of Berkovich analytification $V^{an}$ of $V$. In this talk we will present an analogous construction which provides a model-theoretic counterpart $\widetilde{V}$ of the Huber's analytification of $V$. We show that, the same as for $\widehat{V}$, the space $\widetilde{V}$ is strict pro-definable. Furthermore, we will discuss canonical liftings of the deformation retraction developed by Hrushovski and Loeser. This is a joint project with Pablo Cubides Kovacsics.