Abstract
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.
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This work was supported by the SFB 647 ‘Space-Time-Matter:Arithmetic and Geometric Structures’ of the DFG (German Research Foundation) and by the Spanish grants MTM2013-45935-P (MINECO) and FS/12-2014 (Samuel Solórzano Barruso Foundation).
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Andreas, B., Sánchez Gómez, D. & Sancho de Salas, F. Euler sequence and Koszul complex of a module. Ark Mat 54, 277–297 (2016). https://doi.org/10.1007/s11512-016-0236-4
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DOI: https://doi.org/10.1007/s11512-016-0236-4