Alladi Ramakrishnan Hall

Lower bound on Weil height of algebraic numbers

Sushant Kala

IMSc

A subset $S$ of algebraic numbers satisfies the Bogomolov property if the Weil height on $S$ is bounded below by a positive absolute constant. This property has been extensively studied for various classes of Galois extensions of $\mathbb{Q}$ in the past, and it is known to hold for totally real numbers (Schinzel), maximal abelian extensions of $\mathbb{Q}$ (Amoroso-Dvornicich), and extensions of $\mathbb{Q}$ with bounded local degree (Bombieri-Zannier). In this talk, we formulate a criterion for the Bogomolov property, particularly for non-Galois extensions, which generalizes result of Bombieri and Zannier, and also provides a non-archimedean perspective on the equidistribution of roots. This is joint work with Anup Dixit.