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We apply tilting theory to study modules of finite projective dimension. We introduce the notion of finite and cofinite type for tilting and cotilting classes of modules, respectively, showing that, for each dimension, there is a bijection between these classes and resolving classes of modules.\ud We then focus on Iwanaga-Gorenstein rings. Using tilting theory, we prove the first finitistic dimension conjecture for these rings. Moreover, we characterize them among noetherian rings by the property that Gorenstein injective modules form a tilting class. Finally, we give an explicit construction of families of (co)tilting modules of (co)finite type for one-dimensional commutative Gorenstein ring

a b s t r a c tWe study connections between recollements of the derived category D(Mod R) of a ring R and tilting theory. We first provide constructions of tilting objects from given recollements, recovering several different results from the literature. Secondly, we show how to construct a recollement from a tilting module of projective dimension one. By Nicolás and Saorín (2009) [31], every recollement of D(Mod R) is associated to a differential graded homological epimorphism λ : R → S. We will focus on the case where λ is a homological ring epimorphism or even a universal localization. Our results will be employed in a forthcoming paper in order to investigate stratifications of D(Mod R).

It is well known that a module M over an arbitrary ring admits an indecomposable decomposition whenever it has the property that every local direct summand of M is a direct summand [28]. Recently, J. L. Gómez Pardo and P. Guil Asensio [18] have shown that requiring this property not only for M but for any direct sum M (ℵ) of copies of M even yields the existence of a decomposition of M in modules with local endomorphism ring which, moreover, satisfies many nice properties of decompositions studied in the literature, like the exchange property, or the property of complementing direct summands. More precisely, it turns out that all these properties coincide if, instead of considering a single module M, we pass to the category Add M of all direct summands of direct sums of copies of M.In the present paper, we continue the investigation of these modules calling them modules with perfect decompositions. In Section 1, we show that a module M has a perfect decomposition if and only if for every direct system (M i , f ji ) I of modules in Add M indexed by a totally ordered set I , the canonical epimorphism π : i∈I M i −→ lim − → M i is a split epimorphism. This allows to shed a new light on a number of known examples of modules with perfect decomposition.The remaining sections are devoted to the role played in this context by certain finiteness conditions over the endomorphism ring S = End M. In fact, every module with a perfect decomposition is S-coperfect, that is, it satisfies the descending chain condition on cyclic S-submodules. Actually, in Section 2, we even show that M is -coperfect over S, i.e. any direct sum M (ℵ) of copies of M is S-coperfect.We thus discuss whether the converse implication also holds true. The best answer that we can give in full generality is the following (see Section 3): -coperfectness over the endomorphism ring implies that the pure epimorphism * The second author thanks the D.G.I. of the Spanish Ministry of Science and Technology and the Fundación "Séneca" of Murcia for their financial support.

Abstract. We show that every tilting module of projective dimension one over a ring R is associated in a natural way to the universal localization R → RU at a set U of finitely presented modules of projective dimension one. We then investigate tilting modules of the form RU ⊕ RU /R. Furthermore, we discuss the relationship between universal localization and the localization R → QG given by a perfect Gabriel topology G. Finally, we give some applications to Artin algebras and to Prüfer domains.