报告题目 (Title):Representation theory and noncommutative geometry(表示论和非交换几何)
报告人 (Speaker):林宗柱 教授(美国堪萨斯州立大学)
报告时间 (Time):2025年7月4日(周五)10:00
报告地点 (Place):校本部 GJ303
邀请人(Inviter):张红莲、黄红娣
主办部门:8455新葡萄场网站数学系
报告摘要:Given an affine algebraic scheme X, the closed geometric points are irreducible representations. Let C be the category of quasi-coherent sheaves, which is exactly the category of A-modules if X=Spec(A). Although C is a symmetric monoidal category, Rosenberg gave a reconstruction of the scheme X from the abelian category C. Rosenberg's construction applies to much wider abelian categories (or even exact categories). There is also another reconstruction of X when X is a smooth algebraic variety in terms of the monoidal triangulated tensor category of perfect complexes by Balmer, using thick prime tensor ideals. In this talk I will compare the two constructions when X is a smooth algebraic variety X and propose approaches in noncommutative cases. For not necessarily symmetric triangulated tensor categories, Nakan,Vashaw and Yakimov has constructed a Balmer spectrum. It is an interesting question to compare NVY construction with that of Rosenberg.