Abstract: An algebraic variety X defined over a number field k is called Hilbertian if the set of rational points X(k) is not thin. In other words, rational points on any Zariski dense open subset of X do not lift into any collection of finitely many dominant finite morphisms of degree >1. Clearly the variety X being Hilbertian is stronger than the set X(k) being Zariski dense. This notion originates from constructing finite extensions with prescribed Galois group and goes back to Hilbert and Noether. A conjecture of Corvaja and Zannier predicts that simply connected varieties are Hilbertian. In this talk we report our result which confirms this conjecture for a family of Kummer varieties associated to the jacobians of hyperelliptic curves of genus at least two. This is based on joint work in progress with Damián Gvirtz (UCL).

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ID: 858 9779 5553 
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