Submission date: 11 July 2021

Abstract:

We study the p-adic algebraic groups G from the definable topological-dynamical point of view. We consider the case that M is an arbitrary p-adic closed field and G an algebraic group over ℚ_p admitting an Iwasawa decompostion G=KB, where K is open and definably compact over ℚ_p, and B is a borel subgroup of G over ℚ_p. Our main result is an explicit description of the minimal subflow and Ellis Group of the universal definable G(M)-flow S_G(M^{ext}). We prove that the Ellis group of S_G(M^{ext}) is isomorphic to the Ellis group of S_B(M^{ext}), which is B/B^0.
As applications, we conclude that the Ellis groups corresponding to GL(n,M) and SL(n,M) are isomorphic to \hat ℤ × ℤ_p^*)^n and (\hat ℤ × ℤ_p^*)^{n-1} respectively, generalizing the main result of Penazzi, Pillay, and Yao in Some model theory and topological dynamics of p-adic algebraic groups, Fundamenta Mathematicae, 247 (2019), pp. 191--216.

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Full text arXiv 2107.04963: pdf, ps.