学术报告三十:欧阳毅—On abelian p-ramification torsion modules of quadratic fields

发布时间:2020-11-06

报告时间:2020年11月7日(星期六)9:00-10:00

报告地点翡翠科教楼B座1710室

  

报 告 :欧阳毅 教授

工作单位中国科学技术大学

举办单位:数学学院

报告简介

The abelian p-ramification torsion module of a number field is the p-torsion module of the Galois group of its maximal abelian extension unramified outside p. For p=2, we prove a 4-rank formula and a 4-rank density formula for abelian 2-ramification torsion of imaginary quadratic fields. This is analog to results in 2-class groups of imaginary quadratic fields by Fouvry-Klüners and K-groups of real quadratic by Yue-Yu. We also prove several density results about this group for subfamilies of real and imaginary quadratic fields. Finally, we formulate new Cohen-Lenstra heuristics and extended Cohen-Lenstra heuristics for abelian p-ram torsion modules in quadratic fields and present evidence for our conjectures. This is a joint work with Jianing Li and Yue Xu.

报告人简介

欧阳毅,中国科学技术大学教授,从事数论及其应用研究工作。2000年博士毕业于美国明尼苏达大学,2003年回国,先后在清华大学和中国科学技术大学工作。在数论基础研究和椭圆曲线同源密码等应用研究方面共发表论文30多篇。现任校教学委员会委员,是安徽省教学名师,因华罗庚科技英才班人才培养获中科院和安徽省教学成果奖,获宝钢优秀教师奖。