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On compactly generated torsion pairs and the classification of co-$ t$-structures for commutative noetherian rings


Authors: Jan Šťovíček and David Pospíšil
Journal: Trans. Amer. Math. Soc. 368 (2016), 6325-6361
MSC (2010): Primary 18E30, 13C05; Secondary 18G55, 16E45, 18D10
DOI: https://doi.org/10.1090/tran/6561
Published electronically: December 3, 2015
MathSciNet review: 3461036
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Abstract: We classify compactly generated co-$ t$-structures on the derived category of a commutative noetherian ring. In order to accomplish this, we develop a theory for compactly generated Hom-orthogonal pairs (also known as torsion pairs in the literature) in triangulated categories that resembles Bousfield localization theory. Finally, we show that the category of perfect complexes over a connected commutative noetherian ring admits only the trivial co-$ t$-structures and (de)suspensions of the canonical co-$ t$-structure and use this to describe all silting objects in the category.


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Additional Information

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

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

DOI: https://doi.org/10.1090/tran/6561
Keywords: Commutative noetherian ring, co-$t$-structure, stable derivator, compactly generated Hom-orthogonal pair
Received by editor(s): June 20, 2013
Received by editor(s) in revised form: August 18, 2014
Published electronically: December 3, 2015
Additional Notes: This research was supported by GA ČR P201/12/G028.
Article copyright: © Copyright 2015 American Mathematical Society

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