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arXiv · 2603.10617

Motives, cohomological invariants and the Freudenthal magic square

Nikita Geldhauser·Alexander Henke·Maksim Zhykhovich
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Abstract

We investigate cohomological invariants and motivic invariants of semisimple algebraic groups arising in the Freudenthal magic square. Besides, we show that if the Rost invariant of a strongly inner group of type $E_7$ is a sum of at most two symbols modulo $2$, then it is isotropic over an odd degree field extension, and use this fact to give a different proof of a result of Petrov and Rigby. Moreover, we give a motivic interpretation of a result of Garibaldi and Petersson about a cohomological invariant of degree $5$ for certain groups of type $^2E_6$ which detects their isotropy.

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Nikita Geldhauser, Alexander Henke, Maksim Zhykhovich. 2026-03-11. Motives, cohomological invariants and the Freudenthal magic square. https://arxiv.org/abs/2603.10617

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