Absolute Purity in The Category of Quasi Coherent Sheaves

作者：Aghasi Mansour^*; Nemati Hamidreza

来源：Filomat, 2015, 29(7): 1663-1669.

DOI：10.2298/FIL1507663A

• quasi-coherent sheaf
• absolutely pure
• Fp-injective
• absolutely pure cover

In this paper we consider the class of absolutely pure and Fp-injective quasi-coherent sheaves. We show that these two classes of quasi-coherent sheaves over a locally coherent scheme are equivalent. As a corollary we will show that the class of absolutely pure quasi-coherent sheaves over such a scheme is an enveloping and a covering class. It is proved that over a locally coherent scheme, the pair ((perpendicular to)(Abs(X), Abs(X)) is a cotorsion theory. The existence of a duality between absolutely pure envelopes and flat covers is proved as expected.

• 出版日期2015