The behavior of essential dimension under specializationArticle
Auteurs : 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.
Volume : Volume 6
Publié le : 20 décembre 2022
Accepté le : 20 décembre 2022
Soumis le : 4 janvier 2022
Mots-clés : Mathematics - Algebraic Geometry, 20G10 (Primary) 20G15, 14L30, 13A18 (Secondary)
Financement :
Source : OpenAIRE Graph- Financeur: Natural Sciences and Engineering Research Council of Canada