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Tilting, cotilting, and spectra of commutative noetherian rings


Authors: Lidia Angeleri Hügel, David Pospíšil, Jan Šťovíček and Jan Trlifaj
Journal: Trans. Amer. Math. Soc. 366 (2014), 3487-3517
MSC (2010): Primary 13C05, 13E05, 16D90; Secondary 13C14, 13C60, 13D07, 16E30
DOI: https://doi.org/10.1090/S0002-9947-2014-05904-7
Published electronically: February 6, 2014
MathSciNet review: 3192604
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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.


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Additional Information

Lidia Angeleri Hügel
Affiliation: Dipartimento di Informatica, Settore di Matematica, Università degli Studi di Verona, Strada le Grazie 15 - Ca’ Vignal, 37134 Verona, Italy
Email: lidia.angeleri@univr.it

David Pospíšil
Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Email: pospisil.david@gmail.com

Jan Šťovíček
Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Email: stovicek@karlin.mff.cuni.cz

Jan Trlifaj
Affiliation: Faculty of Mathematics and Physics, Department of Algebra, Charles University, Sokolovská 83, 186 75 Prague 8, Czech Republic
Email: trlifaj@karlin.mff.cuni.cz

DOI: https://doi.org/10.1090/S0002-9947-2014-05904-7
Keywords: Commutative noetherian ring, tilting module, cotilting module, Zariski spectrum, Cohen-Macaulay module
Received by editor(s): March 2, 2012
Received by editor(s) in revised form: June 25, 2012
Published electronically: February 6, 2014
Additional Notes: This research was supported by GAČR 201/09/0816, GAČR 201/09/H012, GAČR P201/10/P084, as well as by MEC-DGESIC (Spain) through Project MTM2008-06201-C02-01, and by the Comissionat Per Universitats i Recerca de la Generalitat de Catalunya through Project 2009 SGR 1389
Article copyright: © Copyright 2014 American Mathematical Society