Number Theory Seminar
Jacob Mayle
UIC
Serre's Open image Theorem and Beyond
Abstract: Let E/Q be an elliptic curve. For each prime number ell, one considers
the mod ell Galois representation of E, which encodes the action of the
absolute Galois group of Q on the ell-torsion subgroup of E. In 1972,
Serre showed that if E is without complex multiplication, then the mod
ell Galois representation is surjective whenever ell is sufficiently
large. In this talk, we'll discuss the theorem, as well as recent
computational and theoretical progress related to it.
Friday January 14, 2022 at 1:00 PM in Zoom