Open Access
April, 2019 Good tilting modules and recollements of derived module categories, II
Hongxing CHEN, Changchang XI
J. Math. Soc. Japan 71(2): 515-554 (April, 2019). DOI: 10.2969/jmsj/78477847


Homological tilting modules of finite projective dimension are investigated. They generalize both classical and good tilting modules of projective dimension at most one, and produce recollements of derived module categories of rings in which generalized localizations of rings are involved. To decide whether a good tilting module is homological, a sufficient and necessary condition is presented in terms of the internal properties of the given tilting module. Consequently, a class of homological, non-trivial, infinitely generated tilting modules of higher projective dimension is constructed, and the first example of an infinitely generated $n$-tilting module which is not homological for each $n \ge 2$ is exhibited. To deal with both tilting and cotilting modules consistently, the notion of weak tilting modules is introduced. Thus similar results for infinitely generated cotilting modules of finite injective dimension are obtained, though dual technique does not work for infinite-dimensional modules.


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Hongxing CHEN. Changchang XI. "Good tilting modules and recollements of derived module categories, II." J. Math. Soc. Japan 71 (2) 515 - 554, April, 2019.


Received: 14 July 2017; Revised: 8 November 2017; Published: April, 2019
First available in Project Euclid: 8 March 2019

zbMATH: 07090054
MathSciNet: MR3943449
Digital Object Identifier: 10.2969/jmsj/78477847

Primary: 13B30 , 16G10 , 18E30
Secondary: 13E05 , 16S10

Keywords: derived category , Gorenstein ring , homological subcategory , recollement , tilting modules , weak tilting modules

Rights: Copyright © 2019 Mathematical Society of Japan

Vol.71 • No. 2 • April, 2019
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