# D. Loughran: Good reduction of complete intersections

Daniel Loughran

**Good reduction of complete intersections**

Thu, Jan. 21, 2016

In 1983, Faltings proved the famous Mordell conjecture on the

finiteness of the set of rational points on curves of higher genus.

Along the way he proved numerous other finiteness statements, including

the Shafarevich conjecture, which states that there are only finitely

many curves of higher genus over a number field up to isomorphism which

have good reduction outside any given set of prime ideals. In this talk

we shall consider analogues of the Shafarevich conjecture for certain

classes of complete intersections in projective space.

This is joint work with Ariyan Javanpeykar (Mainz).