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Transactions of the American Mathematical Society

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

 
 

 

The $ t$-structure induced by an $ n$-tilting module


Author: Silvana Bazzoni
Journal: Trans. Amer. Math. Soc. 371 (2019), 6309-6340
MSC (2010): Primary 18E30; Secondary 18E10, 18E15, 18G55
DOI: https://doi.org/10.1090/tran/7488
Published electronically: August 22, 2018
MathSciNet review: 3937326
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Abstract: We study the $ t$-structure induced by an $ n$-tilting module $ T$ in the derived category $ \mathcal {D}(R)$ of a ring $ R$. Our main objective is to determine when the heart of the $ t$-structure is a Grothendieck category. We obtain characterizations in terms of properties of the module category over the endomorphism ring of $ T$ and, as a main result, we prove that the heart is a Grothendieck category if and only if $ T$ is a pure projective $ R$-module.


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Silvana Bazzoni
Affiliation: Dipartimento di Matematica, Università di Padova, Via Trieste 63, 35121 Padova, Italy
Email: bazzoni@math.unipd.it

DOI: https://doi.org/10.1090/tran/7488
Keywords: Tilting module, $t$-structures, pure projective
Received by editor(s): April 6, 2016
Received by editor(s) in revised form: November 15, 2017
Published electronically: August 22, 2018
Additional Notes: Research was supported by Progetto di Eccellenza Fondazione Cariparo “Algebraic Structures and their applications”.
Article copyright: © Copyright 2018 American Mathematical Society