论文标题
模块类别的可数望远镜猜想的证明
A Proof of the Countable Telescope Conjecture for Module Categories
论文作者
论文摘要
可数望远镜的猜想是在稳定同质理论的框架中出现的，作为一种研究色过滤的工具。但是，事实证明，在模块类别的框架内触发极度肥沃的研究。该项目旨在对萨罗克最近在模块类别的可数望远镜猜想上进行几乎独立的审查。在回忆了一些初步后，我们报告了各种独立兴趣的设备，这将导致上述结果证明。这将是一个特别举止密集的模块系统的家庭的归纳改进的结果，这是我们对地方性的见证。该程序将让人联想到康托尔对角线论点，以实施Shelah的紧凑原则的变体。然后，我们简要审查了刚发展的理论的Enochs猜想的主要应用程序，我们还将陈述其较弱的版本。该项目紧随Saroch的工作（https://link.springer.com/article/10.1007%2FS11856-018-1710-4）;但是，为了完整和简洁，我们稍作修改了一些应用新开发工具的知名证明。
The Countable Telescope Conjecture arose in the framework of stable homotopy theory, as a tool conceived to study the chromatic filtration. It turned out, however, to trigger extremely fertile research within the framework of Module Categories. The project aims at presenting an almost self-contained review of the recent work of Saroch on the Countable Telescope Conjecture for Module Categories. After recalling some preliminaries, we report various devices of independent interest that will lead to a proof of the aforementioned result. This will be the outcome of inductive refinements of families of particularly well-behaved dense systems of modules, our witnessing-notion for localness. The procedure will be reminiscent of Cantor diagonal argument in the implementation of a variant of Shelah's Compactness Principle. Then, we briefly review the main applications to Enochs Conjecture of the just developed theory, and we will also state a weaker version of it. The project closely follows the work of Saroch (https://link.springer.com/article/10.1007%2Fs11856-018-1710-4); however, for the sake of completeness and conciseness, we slightly modified some well-known proofs applying the newly developed tools.
