Stable Domination and Independence in Algebraically Closed Valued Fields
By Deirdre Haskell, Ehud Hrushovski, Dugald Macpherson. 2005
101 citations recorded by the source corpus.
1. Introduction Part I. Stable Domination: 2. Some background on stability theory 3. Definition and basic properties of Stc 4. Invariant types and change of base 5. A combinatorial lemma 6. Strong codes for germs Part II. Independence in ACVF: 7. Some background on algebraically closed valued fields 8. Sequential independence 9. Growth of the stable part 10. Types orthogonal to GAMMA 11. Opacity and prime resolutions 12. Maximally complete fields and domination 13. Invariant types 14. A maximum modulus principle 15. Canonical bases and independence given by modules 16. Other Henselian fields.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/432045f4866f0ff2fb72ce627fa44aeece328246
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
- François Loeser
- Ehud Hrushovski
- Anand Pillay
- David Kazhdan
- Pierre Simon
- Hans Adler
- Julien Sebag
- Qing Liu
In Geometry and Topology
- Ehud Hrushovski
- Hans Adler
- François Loeser
- Pierre Simon
- Anand Pillay
- David Kazhdan
- Julien Sebag
- Johannes Nicaise
In Mathematical Physics
- Ehud Hrushovski
- Hans Adler
- Anand Pillay
- Pierre Simon
- David Kazhdan
- François Loeser
- Johannes Nicaise
- Raf Cluckers
Citations in the corpus
- Introduction to theories without the independence property (2008, background): “Preindependence relations were first defined in my thesis.”
- Non-Archimedean Tame Topology and Stably Dominated Types (2010, background): “18 from [17]:”
- Generically stable and smooth measures in NIP theories (2010, background): “In the theory of algebraically closed valued fields generically stable types coincide with stably dominated types and play a major role in the structural analysis of definable sets [6] as well as in a model-theoretic approach to Berkovich spaces [10].”
- Integration in valued fields (2005, methodology): “We require a variant of a result from [17] on canonical resolutions.”
- On NIP and invariant measures (2007, background): “A special case of a generically stable type is a stably dominated type, as introduced in [9], and our results place those of [9] in the appropriate general context.”