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).
Zoom Information:
Link: https://zoom.us/j/85897795553?pwd=MWdGRVhnTDJiK256b1dNSkZDKzAwdz09
ID: 858 9779 5553
PW: 007574
