Number Theory Seminar

After Mordell's conjecture for curves was proved by Faltings, attentions turn to the distribution of rational and integral points on higher dimensional varieties, which is encoded in the celebrated Vojta's conjecture. Along this line we proved a subspace type inequality, improving the result of Ru-Vojta. Meanwhile, we obtain a sharp criterion of when some certain varieties admit a non-Zariski dense set of integral points. If time permits, I will also discuss possible applications and higher dimensional generalizations. Joint with Keping Huang, Aaron Levin, and with Julie T-Y Wang.