Abstract
We develop techniques to split explicitly the sheaf of principal parts \({\mathcal P^k(\mathcal O(n))}\) as left and right module on the projective line over an arbitrary ring. We then apply the techniques developed to split the principal parts \({\mathcal P^k(\mathcal O(n))}\) for all \({n\,\in {\bf Z}}\) and k ≥ 1 as left and right \({\mathcal O}\)-module on the projective line over any field of characteristic zero giving a complete description of the principal parts on the projective line.
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Maakestad, H. Principal parts on the projective line over arbitrary rings. manuscripta math. 126, 443–464 (2008). https://doi.org/10.1007/s00229-007-0155-6
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DOI: https://doi.org/10.1007/s00229-007-0155-6