In algebraic geometry, a vanishing theorem gives conditions for coherent cohomology groups to vanish. Andreotti–Grauert vanishing theorem Bogomolov–Sommese vanishing theorem Grauert–Riemenschneider vanishing theorem Kawamata–Viehweg vanishing theorem Kodaira vanishing theorem Le Potier's vanishing theorem Mumford vanishing theorem Nakano vanishing theorem Ramanujam vanishing theorem Serre's vanishing theorem Nadel vanishing theorem