Vortrag
Application of mixed Ax-Schanuel to bounding the number of rational points on curves
Vortrag von Dr. Ziyang Gao
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 17.12.18 Zeit: 13.15 - 14.45 Raum: Y27H25
With Philipp Habegger we recently proved a height inequality, using which one can bound the number of rational points on 1-parameter families of curves in terms of the genus, the degree of the number field and the Mordell-Weil rank (but no dependence on the Faltings height). In this talk I will give a blueprint to generalize this method to arbitrary curves. In particular I will focus on: (1) how establishing a criterion for the Betti map to be immersive leads to the desired bound; (2) how to apply mixed Ax-Schanuel to establish such a criterion. This is work in progress, partly joint with Vesselin Dimitrov and Philipp Habegger.