Definable equivariant retractions onto skeleta in non-Archimedean geometry
Basic data for this talk
Type of talk: scientific talk
Name der Vortragenden: Hils, Martin
Date of talk: 28/03/2018
Talk language: English
URL of slides: http://modvac18.math.ens.fr/slides/Hils.pdf
Information about the event
Name of the event: "Model Theory and Applications" (final conference of the trimester "Model Theory, Combinatorics and Valued Fields")
Event period: 26/03/2018 - 30/03/2018
Event location: Institut Henri Poincaré, Paris, Frankreich
Event website: http://modvac18.math.ens.fr/W3.html
Abstract
For a quasi-projective variety Vover a non-archimedean valued field, Hrushovski and Loeser recently introduced a pro-definable space \hat{V}, the stable completion of V, which is a model-theoretic analogue of the Berkovich analytification of V. They showed that \hat{V} admits a pro-definable strong deformation retraction onto a skeleton, i.e., onto a space which is internal to the value group and thus piecewise linear. If the underlying variety is an algebraic group, the group naturally acts on its stable completion by translation. In the talk, we will sketch various ways to construct an S-equivariantpro-definable strong deformation retraction of̂\hat{S} onto a skeleton, in case S is a semiabelian variety. This is joint work with Ehud Hrushovski and Pierre Simon.Keywords: Model Theory; Valued Fields; Non-Archimedean Geometry; Semiabelian Variety; Stable Completion; Berkovich Analytification
Speakers from the University of Münster
| Hils, Martin | Professorship for Mathematical Logic (Prof. Hils) |