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Björn AndreasMathematisches Institut, Freie Universität BerlinDarío Sánchez GómezDepartamento de Matemáticas and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de SalamancaFernando Sancho de SalasDepartamento de Matemáticas and Instituto Universitario de Física Fundamental y Matemáticas (IUFFyM), Universidad de Salamanca
We construct relative and global Euler sequences of a module. We apply it to prove some acyclicity results of the Koszul complex of a module and to compute the cohomology of the sheaves of (relative and absolute) differential $p$ -forms of a projective bundle. In particular we generalize Bott’s formula for the projective space to a projective bundle over a scheme of characteristic zero.