Time：15:00-16:00, Thursday, April 3 2025
Venue：E4-233
Speaker：Nanjun Yang, BIMSA
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. It has been studied by Knebusch in 1970s for real algebraic curves. Over local fields, it naturally relates to 2-dimensional class field theory. Only the case of hyperelliptic curves was considered by Parimala, Arason et. al..
In this talk, we compute explicitly the Witt group of smooth projective curves over nondyadic local fields by reduction, which involves the rationality of Theta characteristics. The case of elliptic curves will be given as an example.
