报告名称：Abelian Galois cohomology of reductive groups I,II

报告专家：田乙胜 副教授

专家所在单位：哈尔滨工业大学

报告时间：2026.01.19，2026.01.20 下午14：00

报告地点:数统楼201报告厅

专家简介： 田乙胜，本科毕业于中国科学技术大学，在法国巴黎萨克雷大学取得博士学位。现为哈尔滨工业大学数学研究院副教授，研究方向为算术几何，包括半整体域上的算术对偶、代数群的Galois上同调、强逼近、弱逼近、局部整体原理等。

报告摘要：In the first talk, we aim to introduce Borovoi's paper "Abelian Galois cohomology of reductive groups". First, we introduce the algebraic fundamental group of Colliot-Thélène and Borovoi. Subsequently,  we briefly recall important facts of (connected) reductive groups. Third, we introduce the abelian Galois cohomology group in degree 0 and 1, and prove that these groups only depend on the algebraic fundamental group of the given reductive group.

In the second talk,, we introduce crossed modules of algebraic groups which enable us to define the abelianization map. Finally, we compute the abelian Galois cohomology for p-adic fields and number fields.