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八秩同辉校庆系列23 Bounded t-structures, finitistic dimensions and singularity categories of triangulated categories

来源: 发布时间: 2024-04-24 点击量:
  • 讲座人: 陈红星 教授
  • 讲座日期: 2024-4-30(周二)
  • 讲座时间: 16:00
  • 地点: 文津楼3211

讲座人简介:

陈红星,首都师范大学数学科学澳门新甫京教授、德国洪堡学者。2021年获国家自然科学基金优秀青年科学基金,曾获教育部学术新人奖,入选北京市科技新星计划,作为主要成员参与两项国家自然科学基金重点项目和一项北京市教育委员会科技计划重点项目。主要从事代数表示论和同调代数的研究,在经典同调猜想(如Nakayama猜想和Tachikawa第二猜想)、导出范畴、无限维倾斜理论等方面取得了一系列的研究成果,如合作解决了关于导出模范畴的Jordan-Holder定理的存在性问题,并系统地建立了无限维倾斜模的导出粘合理论。研究成果发表在Compos.Math., Proc.Lond.Math.Soc., Trans.AMS等国际数学杂志。

讲座简介:

Recently, Amnon Neeman settled a bold conjecture by Antieau, Gepner, and Heller regarding the relationship between the regularity of finite-dimensional noetherian schemes and the existence of bounded t-structures on their derived categories of perfect complexes. In this talk, we establish some very general results about the existence of bounded t-structures on triangulated categories and the invariance of triangulated categories under completion. Our general treatment, when specialized to the case of noetherian schemes, immediately gives us Neeman's theorem as an application and significantly generalizes another remarkable theorem by Neeman about the equivalence of bounded t-structures on bounded derived categories of coherent sheaves. Under mild finiteness assumptions, our results give a categorical obstruction (the singularity category in our sense) to the existence of bounded t-structures on a triangulated category. This reports a recent joint work with Rudradip Biswas, Chris J. Parker, Kabeer Manali Rahul and Junhua Zheng.

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