2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225568Many slope filtrations occur in algebraic geometry, asymptotic analysis, ramification theory, p-adic theories, geometry of numbers... These functorial filtrations, which are indexed by rational (or sometimes real) numbers, have a lot of common properties. We propose a unified abstract treatment of slope filtrations, and survey how new ties between different domains have been woven by dint of deep correspondences between different concrete slope filtrations.Algebraic Geometry11Gxx, 14Dxx, 18Exx, 34Exx, 34Kxxtext