# On a Conjecture by Colliot-Thelene

## Meeting Details

Abstract: Let $f:X \to Y$ be a morphism of varieties over a number field $k$. It is an interesting question to find geometric condition on the morphism $f$ which imply that $f$ is surjective on $p$-adic points for almost all $p$. This question was considered in a systematic way by Colliot-Thelene, who made an explicit conjecture (CCT) about the above to hold. The plan of the talk is to explain the content of CCT and discuss recent results by Denef, Loughran, Skorobogatov, Smeets and even more recent generalizations CCT, e.g. showing that the surjectivity property is a birational property for a wide class of morphisms $f$.