The Shafarevich conjecture for hypersurfaces in abelian varieties

Abstract: Let K be a number field, S a finite set of primes of O_K, and g a positive integer. Shafarevich conjectured, and Faltings proved, that there are only finitely many curves of genus g, defined over K and having good reduction outside S. Analogous results have been proven for other families, replacing "curves of genus g" with "K3 surfaces", "del Pezzo surfaces" etc.; these results are also called Shafarevich conjectures. There are good reasons to expect the Shafarevich conjecture to hold for many families of varieties: the moduli space should have only finitely many integral points.

Will Sawin and I prove this for hypersurfaces in abelian varieties of dimension not equal to 3.

algebraic geometrynumber theory

Audience: researchers in the topic

( paper | slides )

---

MIT number theory seminar

Series comments: To receive announcements by email, add yourself to the nt mailing list.

Past semesters

---