Height functions

Abstract: This talk will be a survey of the theory of heights. We will consider heights for projective varieties over number fields and function fields. We will not only consider finiteness of points of bounded degree and height, but also the number of such points. If time allows, we will consider how the heights associated to different line bundles on a projective variety are related.

algebraic geometrynumber theory

Audience: advanced learners

Comments: The contents of this talk are based on Chapter 2 of the book. Another good source is Lang's book.

---

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.

---