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Preprint Number 1948
1948. John Welliaveetil A study of compatible deformations in non-Archimedean geometry E-mail: Submission date: 23 March 2021 Abstract: In 2010, Hrushovski--Loeser showed that the Berkovich analytification of a quasi-projective variety over a non-Archimedean valued field admits a deformation retraction onto a finite simplicial complex. In this article, we adapt the tools and methods developed by Hrushovski--Loeser to study if such deformation retractions can be obtained to be compatible with respect to a given morphism. Amongst other results, we show that compatible deformation retractions exist over a constructible partition of the base and prove the general statement in the case of a morphism of relative dimension 1 where the target is a smooth connected curve. Mathematics Subject Classification: 03C98, 14G22, 03C64, 14T20 Keywords and phrases: |
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