2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154365This article deals with the Eisenstein classes of Hilbert-Blumenthal families of abelian varieties. We first give a coordinate expression of these one at the topological level, using currents defined by Levin. Then we study the degeneration of these Eisenstein classes at a cusp of the Baily-Borel compactification of the Hilbert-Blumenthal variety. We show, using the explicit description of the Eisenstein classes obtained previously, that these classes degenerate in special values of an $L$-function associated to the underlying totally real number field. We deduce then both a geometric proof the Klingen-Siegel Theorem and a non vanishing result for some of these Eisenstein classes .Constantes rationnelles de la Proposition 4.3 et du Theoreme 5.2 corrigeesNumber Theory14K10, 11G55text