The modules of principal partsPk(E) of a locally free sheaf ε on a smooth schemeX is a sheaf ofOX-bimodules which is locally free as left and rightOX-module. We explicitly split the modules of principal partsPk(O(n)) on the projective line in arbitrary characteristic, as left and rightOp1-modules. We get examples when the splitting-type as left module differs from the splitting-type as right module. We also give examples showing that the splitting-type of the principal parts changes with the characteristic of the base field.
Principal Part Projective Line Base Field Left Module Free Sheaf
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