2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/60704We prove that in odd characteristic the jacobian of a hyperelliptic curve $y^2=f(x)$ has no nontrivial endomorphisms over an algebraic closure of the ground field if the Galois group of the polynomial $f$ of even degree is ``very big". The case of characteristic zero was previously treated by the author (Math. Res. Letters 7(2000), 123--132).LaTeX2e, 6 pagesAlgebraic GeometryNumber Theory14H40; 14K05; 11G30; 11G10text