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 


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© 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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