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理学院专题学术讲座 ∣ Zilong He：On 2-universal integral quadratic forms over local and number fields
时间
2021年6月21日（周一）
10:00-12:00
地点
西湖大学云栖校区4号楼409-411教室
主持
西湖大学理学院 赵以庚 博士
受众
全体师生
分类
学术与研究
理学院专题学术讲座 ∣ Zilong He：On 2-universal integral quadratic forms over local and number fields
时间：2021年6月21日（周一）10:00-12:00
Time：10:00-12:00, Monday, June 21, 2021
地点：西湖大学云栖校区4号楼409-411教室
Venue: Room 409-411, Building 4, Yunqi Campus, Westlake University
主持人：西湖大学理学院 赵以庚 博士
Host: Dr. Yigeng Zhao, School of Science, Westlake University
主讲嘉宾/Speaker：Dr. Zilong He, Southern University of Science and Technology
讲座摘要/Abstract:
Let F be a local field or a number field. An integral indefinite quadratic OF-lattice is n-universal if it represents all integral quadratic OF-lattices of rank n. Suppose F to be a number field. Let L be an integral quadratic OF-lattice. Then we say that L is globally n-universal if L is n-universal. Also, we say that L is locally n-universal if Lp is n-universal for all non-archimedean primes p and FpL represents all quadratic Fp-space of dimension n for all archimedean primes p. Recently, Xu and Zhang studied the case n=1 and gave the necessary and sufficient conditions for an indefinite quadratic form to be locally 1-universal, but not globally. Motivated by their work, we give the equivalence for the case n=2.
In this talk, we will review known results on universal properties for definite quadratic forms and then present our results. Also, we will briefly introduce the representation theory of integral quadratic forms in the dyadic field, developed by Beli, and the theory of spinor genera.
This is a joint work with Hu Yong.
讲座联系人/Contact:
理学院 杨老师 yanghangli@westlake.edu.cn
