Tilting, cotilting, and spectra of commutative noetherian rings
Commutative Algebra
2014-06-03 v3 Category Theory
Rings and Algebras
Representation Theory
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.
Keywords
Cite
@article{arxiv.1203.0907,
title = {Tilting, cotilting, and spectra of commutative noetherian rings},
author = {Lidia Angeleri Hügel and David Pospisil and Jan Stovicek and Jan Trlifaj},
journal= {arXiv preprint arXiv:1203.0907},
year = {2014}
}
Comments
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