Integral points on the ClebschKlein surfaces
Integral points on the ClebschKlein surfaces

Rafael von Känel, Tsinghua University
Fine Hall 214
This talk will be inperson only.
In this talk we present explicit bounds for the Weil height and the number of integral points on classical surfaces first studied by Clebsch (1871) and Klein (1873). Building on Hirzebruch's work in which he related these surfaces to a Hilbert modular surface, we deduced our bounds from a general result for integral points on coarse Hilbert moduli schemes. After explaining this deduction, we discuss the strategy of proof of the general result which combines the method of Faltings (Arakelov, Parsin, Szpiro) with modularity, MasserWuestholz isogeny estimates, and results based on effective analytic estimates and/or Arakelov theory. Joint work with Arno Kret.