  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.
