The behavior of essential dimension under specialization
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2021
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| _version_ | 1866915710056267776 |
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| author | Reichstein, Zinovy Scavia, Federico |
| author_facet | Reichstein, Zinovy Scavia, Federico |
| contents | Let $A$ be a discrete valuation ring with generic point $η$ 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 $η$. We give two applications of this result, one in mixed characteristic, the other in equal characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_12840 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The behavior of essential dimension under specialization Reichstein, Zinovy Scavia, Federico Algebraic Geometry 20G10 (Primary) 20G15, 14L30, 13A18 (Secondary) Let $A$ be a discrete valuation ring with generic point $η$ 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 $η$. We give two applications of this result, one in mixed characteristic, the other in equal characteristic. |
| title | The behavior of essential dimension under specialization |
| topic | Algebraic Geometry 20G10 (Primary) 20G15, 14L30, 13A18 (Secondary) |
| url | https://arxiv.org/abs/2112.12840 |