2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136553We show that the linear dependence on $p$ of the running time of Kedlaya's point-counting algorithm in characteristic $p$ may be reduced to $p^{1/2}$.21 pages; major revision; to appear in International Mathematics Research NoticesNumber Theory11G20; 11-04text