论文标题
模块和复合物的局部，共同体和抗腹性特性在交换环上
Local, colocal, and antilocal properties of modules and complexes over commutative rings
论文作者
论文摘要
本文是对准连续滑轮和准混合半分离方案的同源性滑轮和矛盾的同源性理论的交换代数介绍。抗移位是一种在有限的仿射覆盖物中局部控制全局特性的另一种方式。例如，模块对非额外交换环的注射率并不能由本地化保留，而模块复合物的同型注射率也无法通过定位，即使对于Noetherian环。后者也适用于偏见和合并特性。在交换环上，模块或复合物的所有特性实际上都是抗内周期。如果人们假定偶然的话，它们也是共同体。通常，如果（遗传完整）中的左类是用于交换环的模块或模块复合物的左类理论，则是局部的，并且通过直接图像与仿射浸入浸水有关，则正确的类是抗内部性的。如果对相互调整的模块或相互调整的模块的复合物的合并理论中的右类是共变体的，并且由这种直接图像保存，则左等级是抗内周期的。作为进一步的例子，扁平调整的模块的类别是抗内周，也是相互调整模块的无环，贝克糖隔离或贝克尔 - 对照环形复合物的类别。同样适用于扁平调整模块的平扁平复合物和扁平调节模块的无环络合物，并具有固定的共生模块。
This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are locally controlled in a finite affine open covering. For example, injectivity of modules over non-Noetherian commutative rings is not preserved by localizations, while homotopy injectivity of complexes of modules is not preserved by localizations even for Noetherian rings. The latter also applies to the contraadjustedness and cotorsion properties. All the mentioned properties of modules or complexes over commutative rings are actually antilocal. They are also colocal, if one presumes contraadjustedness. Generally, if the left class in a (hereditary complete) cotorsion theory for modules or complexes of modules over commutative rings is local and preserved by direct images with respect to affine open immersions, then the right class is antilocal. If the right class in a cotorsion theory for contraadjusted modules or complexes of contraadjusted modules is colocal and preserved by such direct images, then the left class is antilocal. As further examples, the class of flat contraadjusted modules is antilocal, and so are the classes of acyclic, Becker-coacyclic, or Becker-contraacyclic complexes of contraadjusted modules. The same applies to the classes of homotopy flat complexes of flat contraadjusted modules and acyclic complexes of flat contraadjusted modules with flat modules of cocycles.
