{"title":"Weight structures and formality","authors":"Coline Emprin, Geoffroy Horel","doi":"arxiv-2406.19142","DOIUrl":null,"url":null,"abstract":"This is a survey on formality results relying on weight structures. A weight\nstructure is a naturally occurring grading on certain differential graded\nalgebras. If this weight satisfies a purity property, one can deduce formality.\nAlgebraic geometry provides us with such weight structures as the cohomology of\nalgebraic varieties tends to present additional structures including a Hodge\nstructure or a Galois action.","PeriodicalId":501119,"journal":{"name":"arXiv - MATH - Algebraic Topology","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.19142","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This is a survey on formality results relying on weight structures. A weight
structure is a naturally occurring grading on certain differential graded
algebras. If this weight satisfies a purity property, one can deduce formality.
Algebraic geometry provides us with such weight structures as the cohomology of
algebraic varieties tends to present additional structures including a Hodge
structure or a Galois action.
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