The Nevo-Zimmer intermediate factor theorem over local fields
  The Nevo-Zimmer theorem classifies the possible intermediate $G$-factors $Y$ in $X \times G/P \to Y \to X$, where $G$ is a higher rank semisimple Lie group, $P$ a minimal parabolic and $X$ an irreducible $G$-space with an invariant probability measure.   An important corollary is the Stuck-Zimmer theorem, which states that a faithful irreducible action of a higher rank Kazhdan semisimple Lie group with an invariant probability measure is either transitive or free, up to a null set.   We present a different proof of the first theorem, that allows us to extend these two well-known theorems to linear groups over arbitrary local fields. 
Arie Levit
math.DS