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arXiv · 2112.12840

The behavior of essential dimension under specialization

Zinovy Reichstein·Federico Scavia
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Abstract

Let $A$ be a discrete valuation ring with generic point $\eta$ and closed point $s$. We show that in a family of torsors over $\operatorname{Spec}(A)$, the essential dimension of the torsor above $s$ is less than or equal to the essential dimension of the torsor above $\eta$. We give two applications of this result, one in mixed characteristic, the other in equal characteristic.

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Zinovy Reichstein, Federico Scavia. 2021-12-23. The behavior of essential dimension under specialization. https://doi.org/10.46298/epiga.2022.8910

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