Submission date: 27 October 2020

Abstract:

We study definable topological dynamics of some algebraic group actions over an arbitrary NIP field K. We show that the Ellis group of the universal definable flow of SL_2(K) is non-trivial if the multiplicative group of K is not type-definably connected, providing a way to find multiple counterexamples to the Ellis group conjecture, particularly in the case of dp-minimal fields. We also study some structure theory of algebraic groups over K with definable f-generics.

Mathematics Subject Classification: 03C45, 54H20

Keywords and phrases:

Full text arXiv 2010.14586: pdf, ps.