发表机构
School of Artificial Intelligence, Jianghan University（江汉大学人工智能学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明交换凝聚环上有限表示模的宽子范畴与完美导出范畴的厚子范畴格同构，构造了逆映射并研究了有限扩张滤过。
AI 中文摘要
本文主要证明了Hovey猜想：对于任意交换凝聚环，有限表示模范畴的宽子范畴格与完美导出范畴的厚子范畴格之间存在格同构。我们为每个有限表示模构造一个有界有限自由复形，其零阶同调为给定模，且其同调位于该模的abelian闭包中。这一实现给出了Hovey对应的逆映射，无需闭包运算。此外，我们研究了有限扩张滤过、它们在环变换下的行为，以及从有限表示模重构任意模的宽子范畴的极限。
英文摘要
In this paper, we mainly prove Hovey's conjecture: for any commutative coherent ring, there is a lattice isomorphism between the lattice of wide subcategories of the category of finitely presented modules and that of thick subcategories of the perfect derived category. We construct, for every finitely presented module, a bounded finite free complex whose zeroth homology is the given module and whose homology lies in its abelian closure. This realization gives an inverse to Hovey's correspondence without a closure operation. In addition, we study finite extension filtrations, their behavior under change of rings, and the limits of reconstructing wide subcategories of arbitrary modules from finitely presented modules.
Comments24 pages
