紧生成三角范畴中厚子范畴的型

Compactly generated triangulated categories are a class of very important and poplular triangulated categories, and all the time it is focused on in the field of representation theory of algebras. At the same time, the thick subcategories play very important and core roles in the researches of substructures and quotient structures of triangulated categories. So this project will be devoted to completely characterize the thick subcategories of compactly generated triangulated categories, which is divided into the following three parts:.1. First, we introduce the notion of types of thick subcategories of compactly generated triangulated categories. Then, from this point of view, we give the complete characterization of thick subcategories of compactly generated triangulated categories and enumerate the specific examples for each type. .2. On the basis of the first part, we further consider the periodicity of type (+infinity ,- infinity) of thick subcategories of compactly generated triangulated categories. The goal is to point out that the periodicities of (+infinity ,- infinity) are finite and to determine all the periodicities with corresponding examples..3. Comparing the types of thick subcategories of compactly generated triangulated categories with the types of Serre subcategories of Grothendieck categories in [FZ], we aim to answer if the types of Serre subcategories of Grothendieck categories would induce the corresponding types of thick subcategories of compactly generated triangulated categories..The project will definitely enrich the theory of triangulated categories.

紧生成三角范畴是一类非常重要且常见的三角范畴， 一直以来都是代数表示论研究的热点问题. 而厚子范畴则是研究三角范畴子结构及商结构的核心工具. 于是本项目将着力刻画紧生成三角范畴中的厚子范畴这一非常重要且基本的对象. 具体分为以下三个部分：.1. 从通过引入紧生成三角范畴中厚子范畴型的概念这一角度, 完成对紧生成三角范畴中厚子范畴的刻画. 并通过实例指出每一型的真实存在性. .2.在第一部分基础上，考虑紧生成三角范畴中型为(+infinity ,- infinity)的厚子范畴的周期性. 旨在回答其周期性是有限的, 并确定其不同周期及给出相应实例..3.比较紧生成三角范畴中厚子范畴的型与Grothendieck范畴中Serre子范畴的型[FZ].旨在阐述Grothendieck范畴中Serre子范畴的型是否可诱导紧生成三角范畴中厚子范畴的相应型..本项目的研究将进一步丰富三角范畴的理论

紧生成三角范畴是一类非常重要且常见的三角范畴，一直以来都是代数表示论研究的热点问题，而厚子范畴则是研究三角范畴子结构及商结构的核心工具。本项目的预定目标是通过伴随函子来定义厚子范畴的型，进而用此来刻画或分类紧生成三角范畴中的厚子范畴这一非常重要且基本的对象。本项目基本上按预定计划推进，未作大幅的调整. 在实现预定研究目标的过程中，我们取得一些好的结果。例如：通过对Grothendieck范畴的进一步研究，发现其上有一种特殊的Quillen模型结构；通过对张量三角范畴和张量范畴及其上相应的Serre子范畴和厚子范畴的研究，发现可将这两种范畴统一抽象出一种新的代数结构。本项目的实施拓宽了前人的研究工作，丰富了abelian 范畴与三角范畴的内容和研究方法。