Abstract
Let k be an algebraically closed field. Using the Eilenberg–Watts theorem over schemes (Nyman, J Pure Appl Algebra 214:1922–1954, 2010), we determine the structure of k-linear right exact direct limit and coherence preserving functors from the category of quasi-coherent sheaves on \(\mathbb{P}^{1}_{k}\) to the category of vector spaces over k. As a consequence, we characterize those functors which are integral transforms.
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Nyman, A. A Structure Theorem for \(\displaystyle\mathbb{P}^{{1}}\) — Spec k-bimodules. Algebr Represent Theor 16, 659–671 (2013). https://doi.org/10.1007/s10468-011-9324-0
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DOI: https://doi.org/10.1007/s10468-011-9324-0