In algebraic geometry, the Ramanujam vanishing theorem is an extension of the Kodaira vanishing theorem due to Ramanujam (1972), that in particular gives conditions for the vanishing of first cohomology groups of coherent sheaves on a surface. The Kawamata–Viehweg vanishing theorem generalizes it.

• Mumford vanishing theorem

• Kawamata, Yujiro (1982), "A generalization of Kodaira-Ramanujam's vanishing theorem", Mathematische Annalen, 261 (1): 43–46, doi:10.1007/BF01456407, ISSN 0025-5831, MR 0675204, S2CID 120101105
• Ramanujam, C. P. (1972), "Remarks on the Kodaira vanishing theorem", J. Indian Math. Soc., New Series, 36: 41–51, MR 0330164
• Laytimi, F.; Nagaraj, D. S. (2018), "Remarks on Ramanujam-Kawamata-Viehweg Vanishing Theorem", Indian Journal of Pure and Applied Mathematics, 49 (2): 257–263, arXiv:1702.04476, doi:10.1007/s13226-018-0267-6, S2CID 256066169

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