2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/98540We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius. For fixed p, the asymptotic running time for a curve of genus g over the field of p^n elements is O(g^{4+ε} n^{3+ε}).10 pages; v2: corrected runtime exponent, added explanation of Lefschetz trace formula, corrected typosAlgebraic GeometryNumber Theory11G20, 11-04text