Equivariant Definable Deformation Retractions in Non-archimedean Geometry

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Abstract

Using the model theory of ACVF, Hrushovski and Loeser established strong topological tameness properties for the Berkovich analytification $V^{an}$ of an algebraic variety $V$. The main work is done for a model-theoretic analogue $\widehat{V}$ of the Berkovich space, whose underlying set is given by the strongly dominated types concentrating on the variety, the main result being the construction of a definable strong deformation retraction of $\widehat{V}$ onto a piecewise linear subspace. In the talk, I will outline the construction of $\widehat{V}$ and then sketch how one may obtain an equivariant version of the main result for a semiabelian variety $S$, namely the existence of a definable strong $S$-equivariant deformation retraction of $\widehat{S}$ onto a piecewise linear group.

Speakers from the University of Münster

Hils, Martin

Professorship for Mathematical Logic (Prof. Hils)