## Séminaire Variétés Rationnelles

### The fibration method over real function fields

#### Ambrus Pál - Imperial College

vendredi 25 janvier 2019 à 15:00
##### Jussieu

Let F be the function field of a smooth, irreducible projective curve over the reals. Let X be a smooth, projective, geometrically irreducible variety equipped with a dominant morphism f onto a smooth projective rational variety with a smooth generic fibre over F. Assume that the cohomological obstruction introduced by Colliot-Thélène is the only one to the local-global principle for rational points for the smooth fibres of f over F-valued points. I will talk about how to show that the same holds for X, too, by adopting the fibration method. Joint work with Endre Szabó.

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