2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161773We introduce the formalism of differential conformal superalgebras, which we show leads to the "correct" automorphism group functor and accompanying descent theory in the conformal setting. As an application, we classify forms of N=2 and N=4 conformal superalgebras by means of Galois cohomology.61 pagesRings and AlgebrasMathematical Physics17B69 (Primary) ; 17B65,12G05,17B81 (Secondary)text