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After the author had completed the work, he was informed that H. J. Tramer had some results upon the cohomology of twisted projective spaces. A part of his results can be seen in Igusa [4].
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Kawasaki, T. Cohomology of twisted projective spaces and lens complexes. Math. Ann. 206, 243–248 (1973). https://doi.org/10.1007/BF01429212
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DOI: https://doi.org/10.1007/BF01429212