Title:
On congruences of Galois representations of number fields

Abstract:
We first explain what Galois representations are and
how they arise in number theory. Then we give a simple
criterion for two l-adic Galois representations of a
number field to be locally isomorphic at a finite place
in terms of their reductions mod l. Such a study is
motivated by the Rasmussen-Tamagawa conjecture on
the finiteness of Abelian varieties with constrained
prime power torsion points.