Sets with few rational points
Appears in collection : Real analytic geometry and trajectories of vector fields / Géométrie analytique réelle et trajectoires de champs de vecteurs
In the spirit of famous papers by Pila & Bombieri and Pila & Wilkie, I will explain how to bound the number of rational points, with respect to their height, in various kinds of sets, such as transcendental sets definable in some o-minimal - or even not o-minimal - structure over the real field. I will emphazise the role played by bounds on derivatives and on sets of zeroes in this context.
