报告人： 杨东 博士（德国斯图加特大学）

题  目：Differential graded algebras and tilting theory.

1. DG categories and triangulated categories.

2. Derived categories of dg algebras and standard functors.

3. Rickard's Morita theorem for derived module categories.

摘  要：Rickard's Morita theorem has been playing a fundamental role in the study of derived module categories.  The aim of this minicourse is to present Keller's elegant proof of Rickard's theorem using dg algebras/categories.

In the first lecture I will introduce dg categories, give a concrete example and show how to obtain triangulated categories from a certain class of dg categories called pre-triangulated dg categories. In the second lecture, I will introduce the dg category of dg modules over a dg algebra, construct the derived category from this dg category and define the derived tensor and Hom functors. In the third lecture I will use the results from the first two lectures to prove Rickard's theorem, following Keller's approach.

时  间： 2012.05.15、18、23日下午15：00-16：40

地  点： 管理科研楼 1611

主办单位：

中国科学技术大学数学科学学院
国家数学与交叉科学中心合肥分中心
中科院吴文俊数学重点实验室