*Time: *Friday, March 09, 2012,
17h30-18h30

*Location: *salle W

## Mordell-Weil Generators for Cubic Surfaces

**Samir Siksek**
(Warwick - Personal website)

Let C be a smooth plane cubic curve over the rationals. The Mordell--Weil Theorem can be restated as follows: there is a finite subset B of rational points such that all rational points can be obtained from this subset by successive tangent and secant constructions. It is conjectured that a minimal such B can be arbitrarily large; this is indeed the well-known conjecture that there are elliptic curves with arbitrarily large ranks. This talk is concerned with the corresponding problem for cubic surfaces.