Tensor functors between categories of quasi-coherent sheaves

Details Tensor functors between categories of quasi-coherent sheaves Tensor functors between categories of quasi-coherent sheaves

2012-02-23

arxiv.org/abs/1202.5147v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

For a quasi-compact quasi-separated scheme X and an arbitrary scheme Y we show that the pullback construction implements an equivalence between the discrete category of morphisms Y --> X and the category of cocontinuous tensor functors Qcoh(X) --> Qcoh(Y). This is an improvement of a result by Lurie and may be interpreted as the statement that algebraic geometry is 2-affine. Moreover, we prove the analogous version of this result for Durov's notion of generalized schemes.

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