2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71324We show here how residue calculus (residue currents, Grothendieck residues, duality theorem) can be used to obtain an algebraic characterization of the Abel-transform of a meromorphic form on germs of analytic sets. We prove by this way a stronger version of Abel-inverse theorem with an "algebraic" approach and we show the link with Wood's theorem. Furthermore, we obtain a new method to bound easily the dimension of the vector space of abelian forms on an algebraic projective hypersurface.33 pages; minor grammatical changes; submitted to Annales de l'Institut FourierComplex VariablesCommutative Algebra32B10;32C30text