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arXiv · 1307.5505

Flat quasi-coherent sheaves of finite cotorsion dimension

Esmaeil Hosseini
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Abstract

Let X be e quasi-compact and semi-separated scheme. If every at quasi- coherent sheaf has finite cotorsion dimension, we prove that X is n-perfect for some n > 0. If X is coherent and n-perfect(not necessarily of finite krull dimension), we prove that every at quasi-coherent sheaf has finite pure injective dimension. Also, we show that there is an equivalence K(PinfX)---> D(FlatX) of homotopy categories, whenever K(PinfX) is the homotopy category of pure injective at quasi-coherent sheaves and D(FlatX) is the pure derived category of at quasi-coherent sheaves.

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Esmaeil Hosseini. 2013-12-03. Flat quasi-coherent sheaves of finite cotorsion dimension. https://arxiv.org/abs/1307.5505

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