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Investigating the Hasse principle for conic bundles

Sam Roven, University of Washington
Tuesday, April 27, 2021 - 10:00am to 10:50am

Have you started thinking about what you will do when quarantine ends? When you are at your next family gathering, what will you do when your distant cousin starts aggressively asking you everything you know about conic bundles and whether or not they satisfy the Hasse principle? In this talk, we discuss answers to this question and more. In particular, we consider special types of conic bundles over \$\mathbb{P}^1\$, known as Châtelet surfaces, and investigate methods for finding rational points on them. We will begin by introducing the Hasse principle, giving some historical results for conic bundles as well as an explicit example. We will additionally discuss some recent results concerning the failure (or lack thereof) of the Hasse principle when we base change to even degree extensions and will illustrate a key part of the proof of these results.

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