Number Theory Commons^™

Galois Representations From Non-Torsion Points On Elliptic Curves, Matthew Phillip Hughes

Senior Projects Spring 2013

Working from well-known results regarding l-adic Galois representations attached to elliptic curves arising from successive preimages of the identity, we consider a natural deformation. Given a non-zero point P on a curve, we investigate the Galois action on the splitting fields of preimages of P under multiplication-by-l maps. We give a group-theoretic structure theorem for the corresponding Galois group, and state a conjecture regarding composita of two such splitting fields.