Application of Koszul duality to commutative algebra

作者将派生范畴的理论（如Koszul对偶）应用于组合交换代数的研究。这个研究项目的主要目的是将这个思想和结果扩展到一般的交换代数。在此方向上，获得了与环相干性相关的结果，并于2009年发表在学术期刊上。在2008年前后，作者稍微改变了研究方向，开始研究组合交换代数中我们无法用常规方法研究的相对较新的对象。在这个方向上，作者已经写了几篇论文。其中一些已经发表在学术期刊上。

The author has been applied the theory of derived categories (e.g., Koszul duality) to the study of combinatorial commutative algebra. The main aim of this research project was to extend this idea and results to general commutative algebra. In this direction, results related to the coherent property of rings were obtained, and the paper was published in an academic journal in 2009. Around 2008, the author slightly changed the direction of the research, and begun to study relatively new objects of combinatorial commutative algebra for which we cannot use usual methods. In this direction, the author has written several papers. Some of them have been published in an academic journal.