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Arboreal Cantor actions.
- Source :
- Journal of the London Mathematical Society; Jun2019, Vol. 99 Issue 3, p678-706, 29p
- Publication Year :
- 2019
-
Abstract
- In this paper, we consider minimal equicontinuous actions of discrete countably generated groups on Cantor sets, obtained from the arboreal representations of absolute Galois groups of fields. In particular, we study the asymptotic discriminant of these actions. The asymptotic discriminant is an invariant obtained by restricting the action to a sequence of nested clopen sets, and studying the isotropies of the enveloping group actions in such restricted systems. An enveloping (Ellis) group of such an action is a profinite group. A large class of actions of profinite groups on Cantor sets is given by arboreal representations of absolute Galois groups of fields. We show how to associate to an arboreal representation an action of a discrete group, and give examples of arboreal representations with stable and wild asymptotic discriminant. [ABSTRACT FROM AUTHOR]
- Subjects :
- PROFINITE groups
CANTOR sets
FINITE fields
DISCRETE groups
CLASS actions
Subjects
Details
- Language :
- English
- ISSN :
- 00246107
- Volume :
- 99
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Journal of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 136784888
- Full Text :
- https://doi.org/10.1112/jlms.12186