{"title":"Recollements of Derived Categories from Two-Term Big Tilting Complexes","authors":"Huabo Xu","doi":"10.1007/s10468-024-10258-w","DOIUrl":null,"url":null,"abstract":"<div><p>We introduce the notion of big tilting complexes over associative rings, which is a simultaneous generalization of good tilting modules and tilting complexes over rings. Given a two-term big tilting complex over an arbitrary associative ring, we show that the derived module category of its (derived) endomorphism ring is a recollement of the one of the given ring and the one of a universal localization of the endomorphism ring. This recollement generalizes the one established for a good tilting module of projective dimension at most one.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10468-024-10258-w","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
We introduce the notion of big tilting complexes over associative rings, which is a simultaneous generalization of good tilting modules and tilting complexes over rings. Given a two-term big tilting complex over an arbitrary associative ring, we show that the derived module category of its (derived) endomorphism ring is a recollement of the one of the given ring and the one of a universal localization of the endomorphism ring. This recollement generalizes the one established for a good tilting module of projective dimension at most one.
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