2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71295This paper concerns towers of curves over a finite field with many rational points, following Garcia--Stichtenoth and Elkies. We present a new method to produce such towers. A key ingredient is the study of algebraic solutions to Fuchsian differential equations modulo $p$. We apply our results to towers of modular curves, and find new asymptotically good towers.Number TheoryAlgebraic Geometry11G20;14H35text