Tilting, cotilting, and spectra of commutative noetherian rings

Abstract

We classify all tilting and cotilting classes over commutative noetherian rings in terms of descending sequences of specialization closed subsets of the Zariski spectrum. Consequently, all resolving subcategories of finitely generated modules of bounded projective dimension are classified. We also relate our results to Hochster's conjecture on the existence of finitely generated maximal Cohen-Macaulay modules.

28 pages; version 2: a citation of the closely related paper arXiv:1202.5605 by Dao and Takahashi added; version 3: minor changes, the proofs of Corollary 4.3 and Theorem 5.10 have been extended and some points in them clarified, and the assumptions of Theorem 5.16 have been made more restrictive

References in corpus (1)

• Classification of resolving subcategories and grade consistent functions

Cited by in corpus (20)

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• Tilting classes over commutative rings
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• Zariski locality of quasi-coherent sheaves associated with tilting
• Tilting and cotilting modules over concealed canonical algebras
• Classifying Resolving Subcategories
• Colocalization and cotilting for commutative noetherian rings
• An explicit self-dual construction of complete cotorsion pairs in the relative context
• Tilting complexes and codimension functions over commutative noetherian rings
• Singular equivalences to locally coherent hearts of commutative noetherian rings
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• Flat Mittag-Leffler modules, and their relative and restricted versions
• Cotilting with balanced big Cohen-Macaulay modules
• On cosilting hearts over the Kronecker algebra
• Flat relative Mittag-Leffler modules and Zariski locality