论文标题
Gorenstein同源性和局部（CO）同源性的有限属性
Gorenstein Homology and Finiteness Properties of Local (Co)homology
论文作者
论文摘要
本文由三章组成。第一章介绍了戈伦斯坦投影和戈伦斯坦的有界复合物。部署相对同源代数的方法，我们分别用投影性和注入性模块的有界复合物近似这种复合物。作为应用程序，我们研究了新的交集定理的Gorenstein版本。 第二章研究了Hartshorne提出的模块和复合物的辅助性概念。招募派生类别的技术，我们彻底研究了这一概念，获得新的结果，并将某些结果扩展到专业集中的稳定性。 第三章深入研究了绿色二元定理，这被广泛认为是对Grothendieck局部二元定理的深远概括。该定理在文献中没有得到解决，因为它值得，其证明确实是一系列分散论文中的纠结的网络。通过仔细审查必要的工具，我们提出了一个明确的记录的该定理的证明。
This thesis is comprised of three chapters. The first chapter deals with bounded complexes of Gorenstein projective and Gorenstein injective modules. Deploying methods of relative homological algebra, we approximate such complexes with bounded complexes of projective and injective modules, respectively. As an application, we investigate the Gorenstein version of the New Intersection Theorem. The second chapter studies the notion of cofiniteness for modules and complexes set forth by Hartshorne. Recruiting techniques of derived category, we study this notion thoroughly, obtain novel results, and extend some of the results to stable under specialization sets. The third chapter delves into the Greenlees-May Duality Theorem which is widely thought of as a far-reaching generalization of the Grothendieck's Local Duality Theorem. This theorem is not addressed in the literature as it merits and its proof is indeed a tangled web in a series of scattered papers. By carefully scrutinizing the requisite tools, we present a clear-cut well-documented proof of this theorem.
