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Non-exactness of direct products of quasi-coherent sheaves. (arXiv:1810.08752v1 [math.CT])

来源于:arXiv
For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct products in the category of quasi-coherent sheaves are not exact unless the scheme is affine. This result can especially be applied to all quasi-projective schemes over commutative noetherian rings. The main tools of the proof are the Gabriel-Popescu embedding and Roos' characterization of Grothendieck categories satisfying Ab6 and Ab4*. 查看全文>>

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