Homological and homotopical aspects of torsion theories - Introduction
Φόρτωση...
Ημερομηνία
Συγγραφείς
Beligiannis, A.
Reiten, I.
Τίτλος Εφημερίδας
Περιοδικό ISSN
Τίτλος τόμου
Εκδότης
American Mathematical Society
Περίληψη
Τύπος
Είδος δημοσίευσης σε συνέδριο
Είδος περιοδικού
peer reviewed
Είδος εκπαιδευτικού υλικού
Όνομα συνεδρίου
Όνομα περιοδικού
Memoirs of the American Mathematical Society
Όνομα βιβλίου
Σειρά βιβλίου
Έκδοση βιβλίου
Συμπληρωματικός/δευτερεύων τίτλος
Περιγραφή
In this paper we investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, t-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is 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. The main focus of our study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand, and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. We also study the connections betweeen torsion theories and closed model structures, which allow us to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance we obtain a classification of (co)tilting modules along these lines. Finally we give torsion theoretic applications to the structure of Gorenstein and Cohen-Ma,caulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.
Περιγραφή
Λέξεις-κλειδιά
torsion pairs, cotorsion pairs, abelian categories, t-structures, triangulated categories, compact objects, tilting theory, derived categories, contravariantly finite subcategories, approximations, stable categories, reflective subcategories, resolving subcategories, closed model structures, cohen-macaulay modules, tate-vogel cohomology, gorenstein rings, contravariantly finite subcategories, auslander-reiten triangles, stable equivalence, abelian categories, triangulated categories, representation-theory, gorenstein algebras, relative homology, tate cohomology, tilting modules
Θεματική κατηγορία
Παραπομπή
Σύνδεσμος
<Go to ISI>://000247277400001
Γλώσσα
en
Εκδίδον τμήμα/τομέας
Όνομα επιβλέποντος
Εξεταστική επιτροπή
Γενική Περιγραφή / Σχόλια
Ίδρυμα και Σχολή/Τμήμα του υποβάλλοντος
Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών