Witt group of nondyadic curves
Organizers
Speaker
Time
Thursday, December 12, 2024 12:15 PM - 1:00 PM
Venue
A4-1
Abstract
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.
Speaker Intro
Nanjun Yang got his doctor and master degree in University of Grenoble-Alpes, advised by Jean Fasel, and bachelor degree in Beihang University. Then he became a postdoc in YMSC. Currently he is a assistant professor in BIMSA. His research interest is the Chow-Witt group of algebraic varieties, with publications on journals such as Camb. J. Math and Ann. K-Theory.