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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Tilting, cotilting, and spectra of commutative noetherian rings
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by Lidia Angeleri Hügel, David Pospíšil, Jan Šťovíček and Jan Trlifaj PDF
Trans. Amer. Math. Soc. 366 (2014), 3487-3517 Request permission

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
  • MR Author ID: 358523
  • 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
  • MR Author ID: 174420
  • ORCID: 0000-0001-5773-8661
  • Email: trlifaj@karlin.mff.cuni.cz
  • 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
  • © Copyright 2014 American Mathematical Society
  • 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
  • MathSciNet review: 3192604