We investigate the assumptions under which a subclass of flat quasicoherent sheaves on a quasicompact and semiseparated scheme allows us to ‘mock’ the homotopy category of projective modules. Our methods are based on module-theoretic properties of the subclass of flat modules involved as well as their behaviour with respect to Zariski localizations. As a consequence we get that, for such schemes, the derived category of flat quasicoherent sheaves is equivalent to the derived category of very flat quasicoherent sheaves. If, in addition, the scheme satisfies the resolution property then both derived categories are equivalent to the derived category of infinite-dimensional vector bundles. The equivalences are inferred from a Quillen equivalence between the corresponding models.

中文翻译：

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公寓派生类别和分辨率性能的 QUILLEN 等效模型

我们研究了在准紧和半分离方案上的扁平准相干滑轮子类允许我们“模拟”射影模的同伦类别的假设。我们的方法基于所涉及的平面模块子类的模块理论属性以及它们在 Zariski 本地化方面的行为。结果我们得到，对于这样的方案，扁平准相干滑轮的派生类别等价于非常扁平准共干滑轮的派生类别。此外，如果该方案满足分辨率属性，则两个派生类别都等价于无限维向量丛的派生类别。等价是从相应模型之间的 Quillen 等价推断出来的。