Mathematische Zeitschrift

, Volume 277, Issue 3–4, pp 847–866 | Cite as

t-Structures and cotilting modules over commutative noetherian rings



For a commutative noetherian ring \(R\), we establish a bijection between the resolving subcategories consisting of finitely generated \(R\)-modules of finite projective dimension and the compactly generated t-structures in the unbounded derived category \(\mathcal {D}(R)\) that contain \(R[1]\) in their heart. Under this bijection, the t-structures \((\mathcal U,\mathcal V)\) such that the aisle \(\mathcal U\) consists of objects with homology concentrated in degrees \(<n\) correspond to the \(n\)-cotilting classes in \({{\mathrm{Mod}\text {-}R}}\). As a consequence of these results, we prove that the little finitistic dimension findim\(R\) of \(R\) equals an integer \(n\) if and only if the direct sum \(\bigoplus _{k=0}^n E_k(R)\) of the first \(n+1\) terms in a minimal injective coresolution \(0\rightarrow R\rightarrow E_0(R)\rightarrow E_1(R)\rightarrow \cdots \) of \(R\) is an injective cogenerator of \({{\mathrm{Mod}\text {-}R}}\).


t-Structure Tilting module Cotilting module Resolving subcategory Finitistic dimension  Gorenstein-injective Gorenstein-flat 

Mathematics Subject Classification (2010)

13D09 13D05 16E30 



We would like to thank Dolors Herbera for showing us Example 4.2. The first named author acknowledges partial support by the University of Padova through Project CPDA105885/10 ”Differential graded categories”, by DGI MICIIN MTM2011-28992-C02-01, and by the Comissionat Per Universitats i Recerca de la Generalitat de Catalunya through Project 2009 SGR 1389. The second named author has been partially supported by the projects MTM2009-20940-C02-02, from the Dirección General de Investigación, and 04555/GERM/06, from the Fundación ’Séneca’ of Murcia, both with a part of FEDER funds.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Università degli Studi di VeronaVeronaItaly
  2. 2.Departamento de MatemáticasUniversidad de MurciaEspinardoSpain

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