Torsors over a diagonal cubic surface

Abstract: Diagonal cubic surfaces are an interesting class of varieties in the context of the Hasse principle, since they have a very simple form and the Brauer-Manin obstruction is conjectured to be the only obstruction to the Hasse principle.

In this and the next talk, we will construct torsors over diagonal cubic surfaces under certain tori that play the role of the universal torsors. We will show that checking whether the Brauer-Manin obstruction is the only one amounts to understanding the Hasse principle on these torsors.

The first talk will focus on the construction of such a torsor.

Reference: Colliot-Thélène, Kanevsky, Sansuc, Arithmétique des surfaces cubiques diagonales, Section 10(a)(b). (English translation)

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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