发表机构
Universita degli Studi di Milano（米兰大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究结合相关结果与方法，证明Artin代数的有限维数有限性是其对立代数的奇点不变量，且有限有限维数可沿奇点范畴的特定完全忠实函子下降，补充了已有相关工作。
AI 中文摘要
我们结合Rickard和Shaul的结果，以及内蕴同调代数方法与纯性理论，证明Artin代数的大有限维数的有限性是其对立代数的奇点范畴通过其模范畴体现的内蕴性质。这种“无对象”方法补充了Dey–Šťovíček的工作，得出相同结论：Artin代数的有限维数的有限性是（对立代数的）奇点不变量。事实上，我们的刻画可用于证明有限有限维数沿奇点范畴间的特定完全忠实函子下降。
英文摘要
We combine results of Rickard and Shaul with methods of intrinsic homological algebra and the theory of purity to prove that the finiteness of the big finitistic dimension of an Artin algebra is an intrinsic property of the singularity category of its opposite algebra, via its category of modules. This `object-free' approach complements work of Dey--Šťovíček and arrives at the same conclusion: the finiteness of the finitistic dimension of Artin algebras is a singular invariant (of the opposite algebras). In fact, our characterisation can be used to prove that finite finitistic dimension descends along certain fully faithful functors between singularity categories. We include an appendix where we explain how our methods can be used to prove non-existence of bounded t-structures on singularity categories.
Comments11 pages. Some new results and revised introduction. Comments are very welcome!
