Torsion points on Elliptic Curves and the Jackson Space

Abstract

In this paper we will use a particular non-commutative scheme to, among other things, study the ramification properties of the field of $p$-torsion points on an elliptic curve and its reduction properties. Also, we show that this non-commutative space also allow us to use the $p$-torsion points to ``parametrise'' classes in the $p$-torsion of the Brauer group of the base field.