{"title":"On conjectures of Sharifi","authors":"T. Fukaya, Kazuya Kato","doi":"10.1215/21562261-2023-0018","DOIUrl":null,"url":null,"abstract":"(1) This talk is about Iwasawa theory. In non-commutative geometry, the field F1, the field of one element (which is still an imaginary existence), is regarded as an important object. The spirit of Iwasawa theory is near to the idea of F1. In the analogy between Z and Fq[T ] (Fq is a finite field), we look for an analogue of F̄q[T ] = Fq[T ]⊗Fq F̄q on the Z-side. The analogue should be Z ⊗F1 F̄1, but this is an imaginary existence. Iwasawa used ∪r≥1Z[ζpr ] (p is a fixed prime number and ζpr is a primitive p-th root of unity) as an analogue of F̄q[T ] on the Z-side.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"27","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyoto Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/21562261-2023-0018","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 27
Abstract
(1) This talk is about Iwasawa theory. In non-commutative geometry, the field F1, the field of one element (which is still an imaginary existence), is regarded as an important object. The spirit of Iwasawa theory is near to the idea of F1. In the analogy between Z and Fq[T ] (Fq is a finite field), we look for an analogue of F̄q[T ] = Fq[T ]⊗Fq F̄q on the Z-side. The analogue should be Z ⊗F1 F̄1, but this is an imaginary existence. Iwasawa used ∪r≥1Z[ζpr ] (p is a fixed prime number and ζpr is a primitive p-th root of unity) as an analogue of F̄q[T ] on the Z-side.
期刊介绍:
The Kyoto Journal of Mathematics publishes original research papers at the forefront of pure mathematics, including surveys that contribute to advances in pure mathematics.