摘要: 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 give a brief introduction to this object and present an alternative approach, based on lovely pairs of valued fields, to study various analytifications using model theory. We will provide 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 and Martin Hils.
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