Bounded t-structures, finitistic dimensions and singularity categories of triangulated categories

发布时间：2024-03-15 作者：浏览次数：

Speaker:	陈红星研究员	DateTime:	2024年3月22日（周五）上午9:20-10:05
Brief Introduction to Speaker: 陈红星，首都师范大学数学科学学院研究员，德国洪堡访问学者。研究方向为代数表示论与同调代数，主要从事经典同调猜想、导出范畴、倾斜与粘合理论等方面的研究。已在Proc. Lond. Math. Soc.，Trans. Amer. Math. Soc.，Int. Math. Res. Not., J. Algebra等国际知名数学杂志发表多篇高水平研究论文。2018年度入选北京市科技新星计划。现正主持国家自然科学基金优秀青年基金项目并参与国家自然科学基金重点项目。		Place:	六号楼二楼报告厅
Abstract: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 (not necessarily algebraic or topological) 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...

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