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- Title
Strongly stably dominated points.
- Authors
Hrushovski, Ehud; Loeser, François
- Abstract
In 8.1 we study further the properties of strongly stably dominated types over valued fields bases. In this setting, strong stability corresponds to a strong form of the Abhyankar property for valuations: the transcendence degrees of the extension and of the residue field extension coincide. In 8.2 we prove a Bertini type result and also that the strongly stable points form a strict ind-definable subset V# of V. In 8.3 we prove a rigidity statement for iso-definable Γ-internal subsets of maximal o-minimal dimension of V, namely that they cannot be deformed by any homotopy leaving appropriate functions invariant. This result will be used in 11.6. In 8.4, we study the closure of iso-definable Γ-internal sets in V# and we prove that V# is exactly the union of all skeleta (using Theorem 11.1.1).
- Subjects
VALUED fields; BERTINI'S theorems; GEOMETRIC rigidity; HOMOTOPY theory; ALGEBRAIC varieties
- Publication
Princeton Annals of Mathematics Studies, 2016, Issue 192, p104
- ISSN
0066-2313
- Publication type
Article