تقرير
Non-archimedean tame topology and stably dominated types
| العنوان: | Non-archimedean tame topology and stably dominated types |
|---|---|
| المؤلفون: | Hrushovski, E., Loeser, F. |
| المصدر: | Annals of Mathematics Studies, 192. Princeton University Press, Princeton, NJ, 2016. vii+216 pp |
| سنة النشر: | 2010 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Logic, 03C65, 03C98, 14G22 (Primary), 03C64, 14T05 (Secondary) |
| الوصف: | Let $V$ be a quasi-projective algebraic variety over a non-archimedean valued field. We introduce topological methods into the model theory of valued fields, define an analogue $\hat {V}$ of the Berkovich analytification $V^{an}$ of $V$, and deduce several new results on Berkovich spaces from it. In particular we show that $V^{an}$ retracts to a finite simplicial complex and is locally contractible, without any smoothness assumption on $V$. When $V$ varies in an algebraic family, we show that the homotopy type of $V^{an}$ takes only a finite number of values. The space $\hat {V}$ is obtained by defining a topology on the pro-definable set of stably dominated types on $V$. The key result is the construction of a pro-definable strong retraction of $\hat {V}$ to an o-minimal subspace, the skeleton, definably homeomorphic to a space definable over the value group with its piecewise linear structure. Comment: Final version |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1009.0252 |
| رقم الأكسشن: | edsarx.1009.0252 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |