2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101265We solve the $σ_2$-Yamabe problem for a non locally conformally flat manifold of dimension $n>8$.31 pages. Final version. To appear in Ann. Sci. École Norm. SupDifferential GeometryAnalysis of PDEs53C20On a fully nonlinear Yamabe problemtext