Witt group of nondyadic curves

BIMSA-YMSC Number Theory Lunch Seminar

Organizers：

Yong Suk Moon, Koji Shimizu

Speaker：

Nanjun Yang

Time：

Thur., 12:00-13:00, Dec. 12, 2024

Venue：

BIMSA A4-1

Title：

Witt group of nondyadic curves

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.