Tilting, cotilting, and spectra of commutative noetherian rings

2012/03/31 by Lidia Angeleri Hügel, David Pospisil, Jan Stovicek +1 · 1 citation
Mathematics · #math.AC #math.CT #math.RA #math.RT #msc:13C05 #msc:13E05 #msc:16D90 #msc:13C14 #msc:13C60 #msc:13D07 #msc:16E30

paper · pdf · doi:10.1090/s0002-9947-2014-05904-7

published as Trans. Amer. Math. Soc. 366 (2014), 3487-3517 · 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

arxiv created 2012/06/29 · arxiv updated 2014/06/03

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.

Citations

• Classification of resolving subcategories and grade consistent functions

Cited by

• Cotilting modules over commutative noetherian rings