Chennai Mathematical Institute


MSc Thesis Talk
15:30 - 16:30, IMSc, Room 326
Points of small height in certain non abelian extensions

Soumyadip Sahu
Chennai Mathematical Institute.


Let $E$ be an elliptic curve without complex multiplication defined over a number field $K$ which has at least one real embedding. The field $F$ generated by all torsion points of $E$ o $K$ is an infinite , non-abelian Galois extension of the ground field which has unbounded, wild ramification above all primes. Following the treatment in Habegger's paper titled " Small Height and Infinite Non abelian Extensions", we prove that the absolute logarithmic Weil height of an element of $F$ is either zero or bounded from below by a positive constant depending only on $E$ and $K$. We also show that the N\'eron-Tate height has a similar gap on $E(F)$.