Witt Group of Nondyadic Curves

Witt group of real algebraic curves has been studied since Knebusch in 1970s. But few results are known if the base field is non-Archimedean except the hyperelliptic case by works of Parimala, Arason et al… In this paper, we compute the derived Witt groups of smooth proper curves over nondyadic local fields with $char\mathrm{\ne }2$ by reduction, with a general study of the existence of Theta characteristics.