Abstract
If X is a quasi-compact and quasi-separated scheme, the category Qcoh(X) of quasi-coherent sheaves on X is locally finitely presented. Therefore categorical flat quasi-coherent sheaves in the sense of Stenström (1968) naturally arise. But there is also the standard definition of flatness in Qcoh(X) from the stalks. So it makes sense to wonder the relationship (if any) between these two notions. In this paper we show that there are plenty of locally finitely presented categories having no other categorical flats than the zero object. As particular instance, we show that Qcoh(𝐏n(R)) has no other categorical flat objects than zero, where R is any commutative ring.
Funding source: DGI
Award Identifier / Grant number: MTM2010-20940-C02-02
Funding source: Fundación Seneca
Award Identifier / Grant number: 04555/GERM/06
© 2015 by De Gruyter
