AI 中文总结
该研究证明了亨泽尔局部环上反变有限预解子范畴的分类，消除了Takahashi定理的Gorenstein假设，还推导了有限CM型Cohen-Macaulay局部环的相关性质，强化了Takahashi猜想。
AI 中文摘要
我们证明，在亨泽尔局部环上，反变有限预解子范畴必为自由模范畴、全模范畴或极大Cohen-Macaulay模子范畴。这消除了Takahashi定理中的Gorenstein假设。我们还证明，除自由模范畴外的有限型预解子范畴必为极大Cohen-Macaulay模子范畴。由此可得，每个有限CM型的Cohen-Macaulay局部环均为一致支配的，从而建立了Takahashi猜想的更强形式。
英文摘要
We show that a contravariantly finite resolving subcategory over a henselian local ring must be the category of free modules or the whole module category or the subcategory of maximal Cohen--Macaulay modules. This removes the Gorenstein assumption from a theorem of Takahashi. We also show that a resolving subcategory of finite type other than the subcategory of free modules must be the subcategory of maximal Cohen--Macaulay modules. As a consequence, every Cohen--Macaulay local ring of finite CM type is uniformly dominant, thereby establishing a stronger form of a conjecture of Takahashi.
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