Arithmetic Study Group: Finiteness results for hypersurfaces over number fields
11 October 2016 14:00 in ES236
Are there only finitely many smooth projective hypersurfaces over the ring of integers? If we fix the degree and dimension and assume the Lang-Vojta conjecture, the answer to this question is positive. In this talk I will explain how one proves the latter statement. Furthermore, I will explain how far one can get with current methods in arithmetic geometry without assuming Lang-Vojta's conjecture. This is joint work with Daniel Loughran (Manchester).