Bertelot猜想和Künneth等晶公式的结晶化身

IF 0.9 1区数学 Q2 MATHEMATICS

Journal of Algebraic Geometry Pub Date : 2018-12-12 DOI:10.1090/jag/789

V. D. Proietto, F. Tonini, Lei Zhang

{"title":"Bertelot猜想和Künneth等晶公式的结晶化身","authors":"V. D. Proietto, F. Tonini, Lei Zhang","doi":"10.1090/jag/789","DOIUrl":null,"url":null,"abstract":"Berthelot’s conjecture predicts that under a proper and smooth morphism of schemes in characteristic \n\n \n p\n p\n \n\n, the higher direct images of an overconvergent \n\n \n F\n F\n \n\n-isocrystal are overconvergent \n\n \n F\n F\n \n\n-isocrystals. In this paper we prove that this is true for crystals up to isogeny. As an application we prove the Künneth formula for the crystalline fundamental group scheme.","PeriodicalId":54887,"journal":{"name":"Journal of Algebraic Geometry","volume":" ","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2018-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A crystalline incarnation of Berthelot’s conjecture and Künneth formula for isocrystals\",\"authors\":\"V. D. Proietto, F. Tonini, Lei Zhang\",\"doi\":\"10.1090/jag/789\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Berthelot’s conjecture predicts that under a proper and smooth morphism of schemes in characteristic \\n\\n \\n p\\n p\\n \\n\\n, the higher direct images of an overconvergent \\n\\n \\n F\\n F\\n \\n\\n-isocrystal are overconvergent \\n\\n \\n F\\n F\\n \\n\\n-isocrystals. In this paper we prove that this is true for crystals up to isogeny. As an application we prove the Künneth formula for the crystalline fundamental group scheme.\",\"PeriodicalId\":54887,\"journal\":{\"name\":\"Journal of Algebraic Geometry\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2018-12-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebraic Geometry\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1090/jag/789\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebraic Geometry","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/jag/789","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 2

摘要

Bertherot猜想预测，在特征p p中的格式的适当光滑态射下，过收敛的F-等晶的较高直接像是过收敛的F-F-等晶。在这篇论文中，我们证明了这对于同成因的晶体是正确的。作为一个应用，我们证明了晶体基群格式的Künneth公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

A crystalline incarnation of Berthelot’s conjecture and Künneth formula for isocrystals

Berthelot’s conjecture predicts that under a proper and smooth morphism of schemes in characteristic p p , the higher direct images of an overconvergent F F -isocrystal are overconvergent F F -isocrystals. In this paper we prove that this is true for crystals up to isogeny. As an application we prove the Künneth formula for the crystalline fundamental group scheme.

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

Journal of Algebraic Geometry 数学-数学

CiteScore

2.70

自引率

5.60%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Algebraic Geometry is devoted to research articles in algebraic geometry, singularity theory, and related subjects such as number theory, commutative algebra, projective geometry, complex geometry, and geometric topology. This journal, published quarterly with articles electronically published individually before appearing in an issue, is distributed by the American Mathematical Society (AMS). In order to take advantage of some features offered for this journal, users will occasionally be linked to pages on the AMS website.