Tilting, cotilting, and spectra of commutative noetherian rings

By Lidia Angeleri Hugel, David Pospíšil, J. Št’ovíček, Jan Trlifaj. 2012

61 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/284b00c70a190e400495c9a28a0d27343cf17ecb

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In Algebra and Number Theory

1. J. Št’ovíček
2. David Pospíšil

In Geometry and Topology

1. J. Št’ovíček
2. David Pospíšil
3. Lidia Angeleri Hugel
4. L. Positselski
5. Jorge Vit'oria
6. James Gillespie
7. Manuel Saor'in
8. Chrysostomos Psaroudakis

In Statistical and Nonlinear Physics

1. David Pospíšil
2. J. Št’ovíček

Citations in the corpus

• On compactly generated torsion pairs and the classification of co--structures for commutative noetherian rings (2012, background): “ to be known without the restrictive assumption ΣX= X. A hint that the answer to Question 3.12 may be positive in the commutative noetherian case is given by the classification of cotilting classes in [3], a relation of which to Hom-orthogonal pairs is discussed more in detail in [4]. 24 JAN ˇSTOVˇ ´”