Mixed-characteristic shtukas

P. Scholze, Jared Weinstein
{"title":"Mixed-characteristic shtukas","authors":"P. Scholze, Jared Weinstein","doi":"10.2307/j.ctvs32rc9.14","DOIUrl":null,"url":null,"abstract":"This chapter looks at mixed-characteristic shtukas. Much of the theory of mixed-characteristic shtukas is motivated by the structures appearing in (integral) p-adic Hodge theory. The chapter assesses Drinfeld's shtukas and local shtukas. In the mixed characteristic setting, X will be replaced with Spa Zp. The test objects S will be drawn from Perf, the category of perfectoid spaces in characteristic p. For an object, a shtuka over S should be a vector bundle over an adic space, together with a Frobenius structure. The product is not meant to be taken literally (if so, one would just recover S), but rather it is to be interpreted as a fiber product over a deeper base. Motivated by this, the chapter then defines an analytic adic space and shows that its associated diamond is the appropriate product of sheaves on Perf.","PeriodicalId":270009,"journal":{"name":"Berkeley Lectures on p-adic Geometry","volume":"603 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mixed-characteristic shtukas\",\"authors\":\"P. Scholze, Jared Weinstein\",\"doi\":\"10.2307/j.ctvs32rc9.14\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This chapter looks at mixed-characteristic shtukas. Much of the theory of mixed-characteristic shtukas is motivated by the structures appearing in (integral) p-adic Hodge theory. The chapter assesses Drinfeld's shtukas and local shtukas. In the mixed characteristic setting, X will be replaced with Spa Zp. The test objects S will be drawn from Perf, the category of perfectoid spaces in characteristic p. For an object, a shtuka over S should be a vector bundle over an adic space, together with a Frobenius structure. The product is not meant to be taken literally (if so, one would just recover S), but rather it is to be interpreted as a fiber product over a deeper base. Motivated by this, the chapter then defines an analytic adic space and shows that its associated diamond is the appropriate product of sheaves on Perf.\",\"PeriodicalId\":270009,\"journal\":{\"name\":\"Berkeley Lectures on p-adic Geometry\",\"volume\":\"603 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Berkeley Lectures on p-adic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2307/j.ctvs32rc9.14\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Berkeley Lectures on p-adic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2307/j.ctvs32rc9.14","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

本章着眼于混合特征的shtuka。许多混合特性的理论是由出现在(积分)p进Hodge理论中的结构所激发的。本章评估了德林菲尔德的小说和当地的小说。在混合特性设置中,X将替换为Spa Zp。测试对象S将从特征p中的完美曲面空间的范畴Perf中提取。对于一个对象,S上的shtuka应该是一个矢量束在一个矢量空间上,并带有一个Frobenius结构。这个产品并不是字面意义上的(如果是这样的话,人们只会恢复S),而是要在更深的基础上解释为纤维产品。在此基础上,本章定义了一个解析进元空间,并证明了其相关的金刚石是Perf上的束的适当积。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Mixed-characteristic shtukas
This chapter looks at mixed-characteristic shtukas. Much of the theory of mixed-characteristic shtukas is motivated by the structures appearing in (integral) p-adic Hodge theory. The chapter assesses Drinfeld's shtukas and local shtukas. In the mixed characteristic setting, X will be replaced with Spa Zp. The test objects S will be drawn from Perf, the category of perfectoid spaces in characteristic p. For an object, a shtuka over S should be a vector bundle over an adic space, together with a Frobenius structure. The product is not meant to be taken literally (if so, one would just recover S), but rather it is to be interpreted as a fiber product over a deeper base. Motivated by this, the chapter then defines an analytic adic space and shows that its associated diamond is the appropriate product of sheaves on Perf.
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
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:604180095
Book学术官方微信