{"title":"The behavior of essential dimension under specialization","authors":"Z. Reichstein, F. Scavia","doi":"10.46298/epiga.2022.8910","DOIUrl":null,"url":null,"abstract":"Let $A$ be a discrete valuation ring with generic point $\\eta$ and closed\npoint $s$. We show that in a family of torsors over $\\operatorname{Spec}(A)$,\nthe essential dimension of the torsor above $s$ is less than or equal to the\nessential dimension of the torsor above $\\eta$. We give two applications of\nthis result, one in mixed characteristic, the other in equal characteristic.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/epiga.2022.8910","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 4
Abstract
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.