报告题目：Hopf algebras and homotopy Lie algebras attached to closed embedding of schemes

报告简介：Let $Z\subseteq X$ be a closed subscheme of a scheme $X$ with a defining ideal sheaf $ \mathcal I\subseteq \mathcal O_X$. The structure sheaf $ \mathcal O_Z$ is a sheaf of $ \mathcal O_X$-modules on $X$ supported on $Z$. The graded sheaves $\mathcal Tor_{*}^{\mathcal O_X}(\mathcal O_Z,\mathcal O_Z)$  and $\mathcal Ext^{*}_{\mathcal O_X}(\mathcal O_Z,\mathcal O_Z$ on $X$ are supported on $Z$ and are quasi-coherent sheaves of $ \mathcal O_Z$-modules. It turns out that $\mathcal Tor_{*}^{\mathcal O_X}(\mathcal O_Z,\mathcal O_Z)$ and $\mathcal Ext^{*}_{\mathcal O_X}(\mathcal O_Z,\mathcal O_Z)$ have Hopf algebra structures (when $X$ is a Noetherian scheme).
    In this talk I will explain how a Koszul-Tate resolution of $ \mathcal O_Z$ in the category of locally free $\mathcal O_X$-modules as a  commutative and cocommutative dg Hopf algebras with divided power structures which gives rise to the Hopf algebra structure on $\mathcal Tor$ and $\mathcal Ext$. In this case there is a sheaf of graded Lie algebras $\mathcal G$ over $\mathcal O_Z$ such that $\mathcal Ext=U(\mathcal G)$. This Lie algebra is called the Homotopy Lie algebras constructed for H-spaces by Milnor-Moore in algebraic topology. This Lie algebra plays the role of tangent complexes. When $Z$ is a complete intersection, this Lie algebra corresponds to obstruction theory in complex algebraic geometry.

报告人： 林宗柱，1989年在美国马萨诸塞大学获得博士学位，师从代数名家James Humphreys, 现为美国堪萨斯州立大学(Kansas State University )终身教授，主要从事表示论的研究，在Invent. Math., Adv. Math, Comm. Math. Phys等顶级数学期刊上发表论文数十篇。

报告时间：202年6月24日（星期二）上午 9：30-10:30

报告地点：数学科学学院617会议室

主办单位：扬州大学数学科学学院

联系人：李立斌 于志强

欢迎广大师生参加！