{"title":"n 堆栈的伽罗瓦对应关系","authors":"Yuxiang Yao","doi":"arxiv-2408.00281","DOIUrl":null,"url":null,"abstract":"We prove a Galois correspondence for $n$-stacks. It gives a correspondence\nbetween the $\\infty$-category of Deligne-Mumford $n$-stacks finite \\'etale over\na connected scheme $X$ and the $\\infty$-category of $n$-stacks of finite sets\nwith an action of the fundamental group of $X$.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"75 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Galois Correspondence for n-Stacks\",\"authors\":\"Yuxiang Yao\",\"doi\":\"arxiv-2408.00281\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a Galois correspondence for $n$-stacks. It gives a correspondence\\nbetween the $\\\\infty$-category of Deligne-Mumford $n$-stacks finite \\\\'etale over\\na connected scheme $X$ and the $\\\\infty$-category of $n$-stacks of finite sets\\nwith an action of the fundamental group of $X$.\",\"PeriodicalId\":501119,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Topology\",\"volume\":\"75 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.00281\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.00281","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove a Galois correspondence for $n$-stacks. It gives a correspondence
between the $\infty$-category of Deligne-Mumford $n$-stacks finite \'etale over
a connected scheme $X$ and the $\infty$-category of $n$-stacks of finite sets
with an action of the fundamental group of $X$.
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