6th of June: Sven Cats

Title: Explicit n(n+1)-descent on elliptic curves 

 Abstract: In order to find generators of large height for the group of rational points on an elliptic curve, the notion of nn-coverings is useful and we will see why one would like to find explicit equations for them for nn as large as possible. To that end, we will describe a procedure to add an nn- and an (n+1)(n+1)-covering to an n(n+1)n(n+1)-covering. This procedure works for all nn but involves working over large field extensions. We will see how to use classical invariant theory to avoid the need for field extensions for n=2n=2, and if time permits discuss extending this to n=3,4n=3,4.