Si M est une sous-varie[acute ]te[acute ] CR ge[acute ]ne[acute ]rique, q-concave de classe C [ i n f i n ] , de codimension re[acute ]elle k d'une varie[acute ]te[acute ] analytique complexe X de dimension n, les complexes de Cauchy-Riemann tangentiels tronque[acute ]s [tau ] [ l e ] q [ m i n u s ] 1 [E p , * ](M), [tau ] [ g e ] n [ m i n u s ] k [ m i n u s ] q + 2 [E p , * ](M) des formes diffe[acute ]rentielles de classe C [ i n f i n ] et [tau ] [ l e ] q [ m i n u s ] 1 [D p , * ](M), [tau ] [ g e ] n [ m i n u s ] k [ m i n u s ] q + 2 [D[prime ] p , * ](M) des courants sur M sont quasi-isomorphes pour 0 [le ] p [le ] n.
Let M be a q-concave CR generic C [ i n f i n ] -smooth submanifold of real codimension k in an n-dimensional complex manifold X, then the truncated tangential Cauchy-Riemann complexes [tau ] [ l e ] q [ m i n u s ] 1 [E p , * ](M), [tau ] [ g e ] n [ m i n u s ] k [ m i n u s ] q + 2 [E p , * ](M) of C [ i n f i n ] -smooth forms and [tau ] [ l e ] q [ m i n u s ] 1 [D[prime ] p , * ](M), [tau ] [ g e ] n [ m i n u s ] k [ m i n u s ] q + 2 [D[prime ] p , * ](M) of currents on M are quasi-isomorphic for 0 [le ] p [le ] n.