The main subject of the course is the arithmetic of elliptic curves. An elliptic curve may be defined as a plane non-singular cubic curve together with a point lying on the curve, or alternatively as an abelian variety of dimension 1 (an algebraic version of a compact Lie group). We shall mainly be concerned with elliptic curves that are defined over fields of arithmetic interest, such as algebraic number fields and finite fields.
Number of hours
2/week
Literature
Milne, Elliptic Curves, available at http://www.jmilne.org/math/Books/index.html
Literature
Silverman, The Arithmetic of Elliptic Curves (Springer GTM)
Examination
TBC
Links
Webpage Elliptic curves