专业化条件下本质维度的行为

Pub Date : 2021-12-23 DOI:10.46298/epiga.2022.8910

Z. Reichstein, F. Scavia

{"title":"专业化条件下本质维度的行为","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":"{\"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}","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

摘要

设$A$是一个具有一般点$\eta$和闭点$s$的离散估值环。我们证明了在$\operatorname{Spec}(a)$上的一组环量中，$ $s$上的环量的本质维数小于或等于$ $\eta$上的环量的本质维数。我们给出了这一结果的两种应用，一种应用于混合特性，另一种应用于等特性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

The behavior of essential dimension under specialization

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.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助