We prove positive-characteristic analogues of certain measure rigidity theorems in characteristic . More specifically, we give a classification result for positive entropy measures on quotients of and a classification of joinings for higher-rank actions on simply connected, absolutely almost simple groups.
"Diagonal actions in positive characteristic." Duke Math. J. 169 (1) 117 - 175, 15 January 2020. https://doi.org/10.1215/00127094-2019-0038