A vanishing theorem for log canonical pairs

Using inversion of adjunction, we deduce from Nadel’s theorem a vanishing property for ideals sheaves on projective varieties, a special case of which recovers a result due to Bertram–Ein–Lazarsfeld. This enables us to generalize to a large class of projective schemes certain bounds on Castelnuovo–Mumford regularity previously obtained by Bertram–Ein–Lazarsfeld in the smooth case and by Chardin–Ulrich for locally complete intersection varieties with rational singularities. Our results are tested on several examples.