Anup Dixit (IMSc)

Number Theory Seminar

Wednesday, May 15th, 2024

Time: 3:30 p.m.  Place: Jeffery Hall, Room 222

Speaker: Anup Dixit (IMSc)

Title: Lower bounds on Weil height for certain infinite non-Galois extensions

Abstract: For a non-zero algebraic number $\alpha$, let $h(\alpha)$ denote its logarithmic Weil height. A classical theorem of Kronecker asserts that $h(\alpha)=0$ if and only if $\alpha$ is a root of unity. For $\alpha$ not a root of unity, it is an important theme to understand lower bounds for $h(\alpha)$. In 2002, Bombieri and Zannier obtained explicit lower bounds on certain infinite Galois extensions in terms of their local degrees. In this talk, we formulate and prove an analogous result for infinite non-Galois extensions. This is joint work with Sushant Kala.