论文标题
大小模块的无限派生类别：天然函子是否完全忠实？
Unbounded derived categories of small and big modules: Is the natural functor fully faithful?
论文作者
论文摘要
考虑所有有限生成的模块的无界派生类别的明显函子，这些模块在所有模块的无界派生类别上都在左Noetherian Ring $ r $上。我们回答了自然的问题，该函子是否在两种特殊情况下具有有限生成的共同体学模块的配合物的完整子类别定义等效性。如果$ r $是无限全局尺寸的准芬罗果环，则该函数不满。如果$ r $具有有限的左全球尺寸，则该函子是等效的。我们还证明了后者对左相干环，Noetherian计划和本地Noetherian Grothendieck类别的变体。
Consider the obvious functor from the unbounded derived category of all finitely generated modules over a left noetherian ring $R$ to the unbounded derived category of all modules. We answer the natural question whether this functor defines an equivalence onto the full subcategory of complexes with finitely generated cohomology modules in two special cases. If $R$ is a quasi-Frobenius ring of infinite global dimension, then this functor is not full. If $R$ has finite left global dimension, this functor is an equivalence. We also prove variants of the latter assertion for left coherent rings, for noetherian schemes and for locally noetherian Grothendieck categories.
