Title: Rationality of conic bundle threefolds over non-closed fields
Abstract: The intermediate Jacobian obstruction to rationality for complex threefolds was introduced by Clemens–Griffiths in their proof of the irrationality of the cubic threefold. For conic bundles over P^2, this obstruction characterizes rationality over the complex numbers. In this talk, we investigate the rationality of these conic bundles over non-closed fields k. We study the recent intermediate Jacobian torsor obstruction of Hassett–Tschinkel and Benoist–Wittenberg, which refines the classical obstruction over C, and we show the failure of this refined intermediate Jacobian torsor obstruction to characterize k-rationality. This talk is based on joint work with S. Frei–S. Sankar–B. Viray–I. Vogt and joint work with M. Ji.