Baker's method

Abstract: In this talk, we will discuss Baker's theorem on lower bounds for linear forms in logarithms, and how it gives effective bounds for quasi-integral points on $\mathbb{P}^1 \setminus \{0,1,\infty\}$. Using coverings, this further yields effective bounds for quasi-integral points on elliptic, superelliptic and certain hyperelliptic affine curves. We will also discuss an application towards finding elliptic curves with good reduction outside a given finite set of places.

Reference: Chapter 8 of Serre, Lectures on the Mordell-Weil theorem.

algebraic geometrynumber theory

Audience: advanced learners

STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Fall 2025 topic: Weil conjectures.

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.