Witt group of nondyadic curves
演讲者
时间
2024年12月12日 12:15 至 13:00
地点
A4-1
摘要
The Witt group of an algebraic variety is the Grothendieck group of vector bundles with non-dengenerate symmetric inner products modulo those with Langrangians. For a field it classifies quadratic forms and is built by extensions of etale cohomologies. For real varieties, it's known to be related to connected components of real points. For curves over local fields, only the case of hyperelliptic curves was considered by Parimala, Arason et. al..
In this talk, we show that Witt group of smooth projective curves over nondyadic local fields is determined by the Picard group, graph of special fiber, splitness of torus and existence of rational points of odd degrees. We compute the case of elliptic curves as an example.
In this talk, we show that Witt group of smooth projective curves over nondyadic local fields is determined by the Picard group, graph of special fiber, splitness of torus and existence of rational points of odd degrees. We compute the case of elliptic curves as an example.
演讲者介绍
杨南君，本科毕业于北京航空航天大学，硕士博士毕业于格勒诺布尔-阿尔卑斯大学，博士导师Jean Fasel。之后在丘成桐数学科学中心做博后，现在是BIMSA的助理研究员。研究方向为代数簇的Chow-Witt群。研究成果发表在Camb. J. Math., Ann. K-Theory等期刊上。