Geodesic
The behavior of essential dimension under specialization
Épijournal de Géométrie Algébrique, Tome 6 (2022)

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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.
DOI : 10.46298/epiga.2022.8910
Classification : 13A18, 14L30, 20G10, 20G15 
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     author = {Reichstein, Zinovy and Scavia, Federico},
     title = {The behavior of essential dimension under specialization},
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     year = {2022},
     doi = {10.46298/epiga.2022.8910},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2022.8910/}
}
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Reichstein, Zinovy; Scavia, Federico. The behavior of essential dimension under specialization. Épijournal de Géométrie Algébrique, Tome 6 (2022). doi: 10.46298/epiga.2022.8910

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