Descent obstruction and the local-global principle for torsors

Abstract: We start with a quick overview of the descent obstruction for the Hasse principle, indicating how torsors and $H^1(k,G)$ show up in this context. Next, we introduce contracted products and twisted torsors, which will be important for us later. Finally, we discuss finiteness results for torsors over local fields and the local-global principle for torsors. These will be useful when we discuss unramified torsors and the descent obstruction in more detail later.

Reference:

1) Poonen, Rational points on varieties, Sections 8.4.7, 5.12.5-5.12.8, and 6.5.6.

2) Skorobogatov, Torsors and rational points, Section 2.2.

algebraic geometrynumber theory

Audience: advanced learners

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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.

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