The Hilbert irreducibility theorem

Abstract: I will introduce the notion of thin sets and discuss some applications to Galois groups of polynomials. Then, I will state and prove Hilbert's irreducibility theorem following Serre's account of Lang's proof.

Reference: Chapter 9 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.