4 papers
Specialization morphisms
Ildar Gaisin, John Welliaveetil
We define the notion of a specialization morphism from a locally noetherian analytic adic space to a scheme. This captures the (classical) specialization morphism associated to a f…
A study of compatible deformations in non-Archimedean geometry
John Welliaveetil
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 finit…
Radiality of definable sets
John Welliaveetil
In this article we use techniques developed by Hrushovski-Loeser to study certain metric properties of the Berkovich analytification of a finite morphism of smooth connected projec…
Constructibility and Reflexivity in non-Archimedean geometry
Ildar Gaisin, John Welliaveetil
We introduce a notion of constructibility for étale sheaves with torsion coefficients over a suitable class of adic spaces. This notion is related to the classical notion of constr…