The Eilenberg-Watts theorem over schemes

Details The Eilenberg-Watts theorem over schemes The Eilenberg-Watts theorem over schemes

2009-02-27

arxiv.org/abs/0902.4886v4

Mathematics

Algebraic Geometry

45 pages. Final version. To appear in J. Pure Appl. Algebra

Scientific paper

We study obstructions to a direct limit preserving right exact functor $F$ between categories of quasi-coherent sheaves on schemes being isomorphic to tensoring with a bimodule. When the domain scheme is affine, or if $F$ is exact, all obstructions vanish and we recover the Eilenberg-Watts Theorem. This result is crucial to the proof that the noncommutative Hirzebruch surfaces constructed by C. Ingalls and D. Patrick are noncommutative $\mathbb{P}^{1}$-bundles in the sense of M. Van den Bergh.

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