Lovely pairs of valued fields and adic spaces

Abstract: 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.

algebraic geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Comments: The talk will be given in the offline + online duplex mode.

Zoom ID: 649 4104 826

Passowrd: 143688

Link: zoom.com.cn/j/64941048264?pwd=aUI5ZWQvbTYwVmlEekowZ0w0eTZ4UT09

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POINTS - Peking Online International Number Theory Seminar

Series comments: Description: Seminar on number theory and related topics

This seminar series is sponsored by the Beijing International Center of Mathematical Research (BICMR) and the School of Mathematical Sciences of Peking University.

The conference number and password are available on the external website. See also the announcements on bicmr.pku.edu.cn

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