## Zinovy Reichstein ; Federico Scavia - The behavior of essential dimension under specialization

epiga:8910 - Épijournal de Géométrie Algébrique, December 20, 2022, Volume 6 - https://doi.org/10.46298/epiga.2022.8910
The behavior of essential dimension under specialization

Authors: 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
Published on: December 20, 2022
Accepted on: December 20, 2022
Submitted on: January 4, 2022
Keywords: Mathematics - Algebraic Geometry,20G10 (Primary) 20G15, 14L30, 13A18 (Secondary)