{"title":"Moduli of local shtukas and Harris’s\nconjecture","authors":"D. Hansen","doi":"10.2140/tunis.2021.3.749","DOIUrl":null,"url":null,"abstract":"We prove, under a certain assumption of “Hodge-Newton reducibility”, a strong form of a conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local shtukas for GLn. Our strategy is roughly based on a previous strategy developed by Mantovan in the setting of p-divisible groups, but the arguments are completely different. In particular, we reinterpret and generalize the Hodge-Newton filtration of a p-divisible group in terms of modified vector bundles on the Fargues-Fontaine curve. We also compute the dualizing complex and compactly supported étale cohomology of any positive Banach-Colmez space over any base; this should be of independent interest.","PeriodicalId":36030,"journal":{"name":"Tunisian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-10-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Tunisian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/tunis.2021.3.749","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 7
Abstract
We prove, under a certain assumption of “Hodge-Newton reducibility”, a strong form of a conjecture of Harris on the cohomology of moduli spaces of mixed-characteristic local shtukas for GLn. Our strategy is roughly based on a previous strategy developed by Mantovan in the setting of p-divisible groups, but the arguments are completely different. In particular, we reinterpret and generalize the Hodge-Newton filtration of a p-divisible group in terms of modified vector bundles on the Fargues-Fontaine curve. We also compute the dualizing complex and compactly supported étale cohomology of any positive Banach-Colmez space over any base; this should be of independent interest.