{"title":"Cotangent bundles and micro-supports in mixed characteristic case","authors":"Takeshi Saito","doi":"10.2140/ant.2022.16.335","DOIUrl":null,"url":null,"abstract":"For a regular scheme and its reduced closed subscheme, the latter being of finite type over a perfect field of positive characteristic, we define its cotangent bundle restricted to the closed subscheme as a family of vector bundles on smooth schemes over the field endowed with morphisms to the closed subscheme factoring through the Frobenius. For a constructible complex on the etale site of the scheme, we introduce the condition to be micro-supported on a closed conical subset in the cotangent bundle. We compute the singular supports of certain Kummer sheaves of rank 1.","PeriodicalId":278201,"journal":{"name":"arXiv: Algebraic Geometry","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/ant.2022.16.335","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
For a regular scheme and its reduced closed subscheme, the latter being of finite type over a perfect field of positive characteristic, we define its cotangent bundle restricted to the closed subscheme as a family of vector bundles on smooth schemes over the field endowed with morphisms to the closed subscheme factoring through the Frobenius. For a constructible complex on the etale site of the scheme, we introduce the condition to be micro-supported on a closed conical subset in the cotangent bundle. We compute the singular supports of certain Kummer sheaves of rank 1.