On analytification over henselian valued fields

Abstract: Berkovich's analytification of an algebraic variety admits a model-theoretic avatar, due to Hrushovski and Loeser: the space of stably dominated types, equivalently the definable types orthogonal to the value group, working in ACVF, the theory of algebraically closed valued fields. In this talk I will describe a common framework for analytification over a broad class of henselian valued fields of equicharacteristic zero for which the right object is again the space of definable types orthogonal to the value group. We realize this space inside a space of hyperfield points, following a construction due to J. Jun. A single construction thereby recovers the Hrushovski–Loeser analytification and the real analytification of Jell, Scheiderer and Yu, and yields a new analytification of $p$-adic semialgebraic sets. This is joint work with Mariana Vicaría and Jinhe Ye.

algebraic geometrylogicnumber theory

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic