Title: Homological Aspects of Torsion Theories.
       Preprint, (2001).

Authors: A. Beligiannis and I. Reiten.

Addresses: Department of Mathematics, University of the Aegean,
           83200 Karlovassi, Samos, Greece.

           Department of Mathematical Sciences,
           Norwegian University of Science and Technology,
           7490 Trondheim, Norway.


\begin{abstract}
 In this paper we study torsion theories in the general setting of
pretriangulated categories, an omnipresent class of additive
categories which includes abelian, triangulated, stable, and more
generally  (homotopy categories of) closed model categories in the
sense of Quillen, as special cases.

 We explore the formal analogies of the concept of a torsion theory
in the above settings, concentrating our study  to the
relationship between orthogonal subcategories and the existence of
left or right adjoints in connection with their interaction with
the  structure of left/right triangles and exact sequences.

 The main focus of our study lies to the investigation of the
strong connections and the interplay between torsion theories and
tilting theory in abelian, triangulated and stable categories. The
proper setting for the formulation of these connections is via
closed model structures. We also study (co)homological functors
induced by torsion theories,  thus generalizing the Tate-Vogel
(co)homological functors, and we give applications to the
structure of the representations of Artin algebras and Gorenstein
rings.
\end{abstract}