The behavior of essential dimension under specializationArticle
Authors: Zinovy Reichstein ; Federico Scavia
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Zinovy Reichstein;Federico Scavia
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.