报告时间：2022/06/11 10:00-11:00

腾讯会议：438-298-320

报告题目：Derived decompositions of abelian categories

摘要：Semi-orthogonal decompositions of the derived categories of abelian categories are widely used in different branches of mathematics. For example, in algebraic geometry to study Fourier-Mukai transforms on derived categories of coherent sheaves, and in homotopy theory to get $t$-structures of triangulated categories. A fundamental question is how to get such  decompositions. In this talk, we shall present a sufficient and necessary condition to construct such decompositions. Compared with the definition of orthogonal decompositions, the criterion is given in terms of subcategories of given abelian categories, instead of in terms of derived subcategories, and can be applied to many situations, such as localizing subcategories, homological ring epimorphisms, commutative noetherian rings and non-singular rings. This reports a joint work with H.X. Chen.

报告人简介：惠昌常，首都师范大学数学科学学院教授、博士生导师。曾获教育部科技进步二等奖，德国“年轻杰出学者洪堡奖”, 教育部长江学者特聘教授。长期从事代数表示论和同调代数理论相关的研究工作，在Math. Ann., Adv. Math.等国内外重要学术期刊发表论文90多篇;先后主持国家自然科学基金重点项目、高等学校博士学科点专项基金等，现为J. Algebra、Arch. Math.等杂志的编委。