| Résume | I will discuss recent progressusing additive combinatorics to provethe Hasse principle and weak approximation for certain varietiesdefined by systems of equations involving norm forms. This allows usto show that the Brauer-Manin obstruction controls weak approximationon normic bundles of the shape $N_K(x_1,...,x_n) = P(t)$, where $P(t)$isa product of linear polynomials all defined over $\mathbf Q$ and$K/\mathbf Q$ is anarbitrary extension of degree~$n$.This is joint work with Tim Browning. |
