A structure theorem for P^1-Spec k-bimodules

Abstract

Let k be an algebraically closed field. Using the Eilenberg-Watts theorem over schemes, we determine the structure of k-linear right exact direct limit and coherence preserving functors from the category of quasi-coherent sheaves on P^1_k to the category of vector spaces over k. As a consequence, we characterize those functors which are integral transforms.

12 pages. Minor changes. Final version, to appear in Algebr. Represent. Theory