Torsors of algebraic groups over fields

Abstract: To build towards the descent obstruction, we begin by defining torsors. In this talk, we introduce $G$-torsors under smooth algebraic group $G/k$ as a generalization of simply transitive $G$-sets of group $G$. We discuss its classification and some results that arise from it, laying the foundation for understanding them over arbitrary bases.

Reference: Poonen, Rational points on varieties, Section 5.12.

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.