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arXiv · 2401.08532

Essential dimension of cohomology classes via valuation theory

Danny Ofek·Zinovy Reichstein
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Abstract

We give a formula for the essential dimension of a cohomology class $\alpha$ in $H^d(K, \mathbb{Q}_p/\mathbb{Z}_p (d))$ when $K$ is a strictly Henselian field. This formula is particularly explicit in the case, where $\alpha$ is a Brauer class (for $d = 2$). As an application of our bound with $d = 3$, we study the essential dimension of exceptional groups by examining the image of the Rost invariant.

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Danny Ofek, Zinovy Reichstein. 2024-01-16. Essential dimension of cohomology classes via valuation theory. https://arxiv.org/abs/2401.08532

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