2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/105132We introduce non-abelian cohomology sets of Hopf algebras with coefficients in Hopf modules. We prove that these sets generalize Serre's non-abelian group cohomology theory. Using descent techniques, we establish that our construction enables to classify as well twisted forms for modules over Hopf-Galois extensions as torsors over Hopf-modules.19 pagesK-Theory and HomologyRings and Algebras18G50text