One-tilting classes and modules over commutative rings
By Michal Hrbek. 2015
51 citations recorded by the source corpus.
Abstract 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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/51b34f9f7c2967d3aeabd6d7d43f269ec5107fb8
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In Algebra and Number Theory
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Silting modules over commutative rings (2016, methodology): “re we give a direct proof by providing an explicit construction for a silting module corresponding to a Gabriel filter of finite type. It generalises the construction of a Fuchs-Salce tilting module in [12]. Construction 4.5. Let Rbe a commutative ring and Ga Gabriel filter of finite type. Let Ibe the c”