The Shafarevich conjecture for hypersurfaces

Time: Thursday, July 23, from 4:30pm to 6:30pm (Hanoi time)

Onlline: (Join Zoom Meeting) tại https://zoom.us/j/99636681387?pwd=0WscBnehOJig68SqctGluVuA3RwraE.1

Abstract: At the ICM 1962, Shafarevich proposed the following conjecture: over any number field, there are only a finite number of isomorphism classes of smooth projective curves of genus g ≥ 2 with good reduction outside a given finite set of places. Since then, analogous statements for other types of varieties are known as instances of the Shafarevich conjecture. The Shafarevich conjecture is partly verified by Lawrence-Venkatesh [1] for hypersurfaces in projective spaces over Q, and is fully proved by Lawrence-Sawin [2] for hypersurfaces in abelian varieties. In this talk, we will discuss the Shafarevich conjecture for hypersurface sections of a smooth projective variety over an arbitrary number field, following the method of [1] and [2].

References:

1. Brian Lawrence and Akshay Venkatesh. Diophantine problems and p-adic period mappings. Invent. Math., 221(3):893–999, 2020.
2. Brian Lawrence and Will Sawin. The Shafarevich conjecture for hypersurfaces in abelian varieties. Annals of Mathematics, 202(3):857 – 1000, 2025.