This week's seminars
Arithmetic Study Group: Wieferich statistics, p-adic integrals and rational points on curves.
10 December 2019 13:00 in CM219
A Wieferich prime is a prime number p such that 2^(p-1) is congruent to 1 modulo p^2. These numbers originally arose in the context of Fermat's last theorem. At present very little is known about them, although there are some conjectures. One can analogously define Wieferich primes for 3, or 5, or for a point on an abelian variety. In this talk I will explain what Wieferich primes for abelian varieties have to do with p-adic integrals and rational points on curves, and will also describe some (unconditional) results on the heights of rational points on higher genus curves.