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).