{"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}
引用次数: 2
Abstract
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.
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.
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