One-tilting classes and modules over commutative rings

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• 作者：Michal Hrbek¹ ; ^{hrbmich@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 13C05 ; 13D30 ; 16D90 ; secondary ; 16E30 ; 13D07 ; 13B30
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 September 2016
• 年：2016
• 卷：462
• 期：Complete
• 页码：1-22
• 全文大小：490 K

文摘

We classify 1-tilting classes over an arbitrary commutative ring. As a consequence, we classify all resolving subcategories of finitely presented modules of projective dimension at most 1. Both these collections are in 1-1 correspondence with faithful Gabriel topologies of finite type, or equivalently, with Thomason subsets of the spectrum avoiding a set of primes associated in a specific way to the ring. We also provide a generalization of the classical Fuchs and Salce tilting modules, and classify the equivalence classes of all 1-tilting modules. Finally we characterize the cases when tilting modules arise from perfect localizations.