2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68799Let $k$ be a field, $C\to \Spec k$ be a stable curve and let $G$ be a finite group acting faithfully on the curve $C\to \Spec k$. In this article, we compute the vector space $\Ext^1_G(Ω_{C/k}, Ø_C)$, the sheaf $Ω_{C/k}$ being the sheaf of relative differentials. This vector space is naturally isomorphic to the set of first order $G$-equivariant deformations of $C$. The computation we do here will be used in a future article.31 pages, frenchAlgebraic GeometryNumber Theory14H30text