{"title":"Fourier–Mukai transforms commuting with Frobenius","authors":"Daniel Bragg","doi":"10.1112/blms.13145","DOIUrl":null,"url":null,"abstract":"<p>We show that a Fourier–Mukai equivalence between smooth projective varieties of characteristic <span></span><math>\n <semantics>\n <mi>p</mi>\n <annotation>$p$</annotation>\n </semantics></math> that commutes with either pushforward or pullback along Frobenius is a composition of shifts, isomorphisms, and tensor products with invertible sheaves whose <span></span><math>\n <semantics>\n <mrow>\n <mo>(</mo>\n <mi>p</mi>\n <mo>−</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$(p-1)$</annotation>\n </semantics></math>th tensor power is trivial.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"56 11","pages":"3477-3483"},"PeriodicalIF":0.8000,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.13145","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the London Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/blms.13145","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
We show that a Fourier–Mukai equivalence between smooth projective varieties of characteristic that commutes with either pushforward or pullback along Frobenius is a composition of shifts, isomorphisms, and tensor products with invertible sheaves whose th tensor power is trivial.
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