1er étage bâtiment Braconnier, Université Claude Bernard Lyon 1 - La Doua
(Joint work with Olivier Benoist.) The Lüroth problem asks whether
unirational varieties are rational. It has a positive answer for complex
curves and surfaces; negative answers for complex threefolds have been
understood since the 70's. I will discuss the Lüroth problem for real
algebraic varieties that are geometrically rational and explain a
counterexample not accounted for by the topology of the real locus or by
a nontrivial unramified cohomology group over the reals.