Some model theory and topological dynamics of p-adic algebraic groups

We study p-adic algebraic groups G from the “stability-theoretic” and topological-dynamical points of view, that is we consider invariants of the action of G on its space of types over Qp in the language of fields. Our main focus is when G = SL(2,Qp) where we identify minimal subflows as well as the Ellis group. But we also touch on related cases such as the additive and multiplicative groups, the Borel subgroup B(Qp) of G, SL2(Zp), as well as the action of SL(2,Qp) on the type space of the projective line over Qp.1 Introduction and preliminaries