Finite descent on curves I

Abstract: In this and the next talk, we're focusing on the descents of finite étale group schemes, and similar properties over finite solvable and abelian group schemes. We discuss on the subset of adelic points cut by these covering conditions, and about their relation with the rational points on the variety. We would further relate these obstruction with the Brauer-Manin obstruction, and develop results over curves.

Reference: Stoll, Finite Descent Obstructions and Rational Points on Curves, Section 5-6 (note the erratum)

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.

Spring 2026 topic: The descent obstruction.

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.