发表机构
University of Arkansas; University of Texas Rio Grande Valley; Florida A&M University（阿肯色大学; 德克萨斯大学里奥格兰德河谷分校; 佛罗里达农工大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明交换诺特环上有限完全交维数模具有有限拟射影维数，改编Bergh技术并给出内射版本及局部化行为的回答。
AI 中文摘要
我们证明，在交换诺特环上，每个具有有限完全交维数的有限生成模都具有有限的拟射影维数。我们的证明改编了Bergh的降低复杂度技术，该技术最初用于证明局部环上有限完全交维数复形的虚拟小性，通过逐步扩大锥的完美轨迹并控制其同调来实现。这肯定地回答了Jorgensen、Takahashi和第三作者提出的问题的一部分。我们还为具有对偶复形的环建立了我们结果的对偶内射版本。最后，我们证明，在这样的环上，文献中出现的完全交维数的三个内射类比对于具有有限生成同调的有界复形是一致的，而其中两个即使没有对偶复形也一致。我们还给出了一个例子表明有限生成假设是必要的，从而完整回答了Sather-Wagstaff的问题。我们最后研究了这些维数的局部化行为，部分回答了Sather-Wagstaff和Totushek的问题。
英文摘要
We prove that, over a commutative Noetherian ring, every finitely generated module of finite complete intersection dimension has finite quasi-projective dimension. Our proof adapts Bergh's technique of reducing complexity, originally used to establish virtual smallness for complexes of finite complete intersection dimension over local rings, by successively enlarging the perfect locus of the cones and controlling their homology. This gives an affirmative answer to part of a question of Jorgensen, Takahashi, and the third author. We also establish a dual injective version of our result for rings admitting a dualizing complex. Finally, we show that, over such rings, the three injective analogues of complete intersection dimension appearing in the literature coincide for bounded complexes with finitely generated homology, while two of them coincide even without a dualizing complex. We also give an example showing that the finite-generation hypothesis is necessary, thereby providing a full answer to a question of Sather-Wagstaff. We conclude by studying the localization behavior of these dimensions, obtaining a partial answer to a question of Sather-Wagstaff and Totushek.
