标题： 纯内射平坦的同伦范畴与格罗滕迪克对偶性 显示英文标题

标题： The homotopy category of pure injective flats and Grothendieck duality

摘要： 设 (X;OX) 是一个具有对偶复形 D 的局部诺特概形。我们证明 DOX - : K(PinfX)----> K(InjX) 是三角范畴之间的等价，其中 K(InjX) 是注入的准凝聚 OX-模的同伦范畴，K(PinfX) 是纯注入平坦准凝聚 OX-模的同伦范畴。 当 X 是仿射时，我们证明这个等价是格罗滕迪克对偶定理的无限完备化。 此外，我们证明 D OX - 在平坦的纯导出范畴和绝对纯准凝聚 OX-模的纯导出范畴之间诱导一个等价。 显示英文摘要

摘要： Let (X;OX) be a locally noetherian scheme with a dualizing complex D. We prove that DOX - : K(PinfX)----> K(InjX) is an equivalence of triangulated categories where K(InjX) is the homotopy category of injective quasi-coherent OX- modules and K(PinfX) is the homotopy category of pure injective flat quasi-coherent OX-modules. Where X is affine, we show that this equivalence is the infinite completion of the Grothendieck duality theorem. Furthermore, we prove that D OX - induces an equivalence between the pure derived category of flats and the pure derived category of absolutely pure quasi-coherent OX-modules.