Unit:
Department of MathematicsLibrary of the School of Science
Dissertation committee:
Ιωάννης Εμμανουήλ Καθηγητής Τμήμα Μαθηματικών, ΕΚΠΑ,
Μιχαήλ Μαλιάκας Καθηγητής Τμήμα Μαθηματικών, ΕΚΠΑ,
Απόστολος Μπεληγιάννης Καθηγητής Τμήμα Μαθηματικών, Πανεπιστήμιο Ιωαννίνων,
Ιωάννης Ντόκας Επίκ. Καθηγητής Τμήμα Μαθηματικών, ΕΚΠΑ,
Μιχαήλ Συκιώτης Αναπλ. Καθηγητής Τμήμα Μαθηματικών, ΕΚΠΑ,
Ολυμπία Ταλέλλη Ομότιμη Καθηγήτρια Τμήμα Μαθηματικών, ΕΚΠΑ
Χρυσόστομος Ψαρουδάκης Αναπληρωτής Καθηγητής Τμήμα Μαθηματικών, Α.Π.Θ.,
Original Title:
Κ-absolutely pure συμπλέγματα και Ευσταθείς κατηγορίες στη Gorenstein Ομολογική ΄Αλγεβρα
Translated title:
Κ-absolutely pure complexes and Stables categories in Gorenstein Homological Algebra
Summary:
We examine the class of K-absolutely pure complexes. These arethe complexes which are right orthogonal in the homotopy category K(R) to the acyclic complexes of pure-projective modules. The class K-abspure of these complexes is preenvelopingin K(R); in fact, a Bousfield localization exists for the embedding K-abspure ⊆ K(R) andthe quotient K(R)/K-abspure is equivalent to the homotopy category of acyclic complexesof pure-projective modules. We examine the role of K-absolutely pure complexes in the purederived category Dpure(R) and show that K-abspure is the isomorphic closure of the classof K-injective complexes therein. We explore the relevance of strongly fp-injective modulesin the study of K-absolutely pure complexes and characterize the K-absolutely pure complexes of strongly fp-injective modules. The notion of K-absolute purity isdual to the notion of K-flatness in the homotopy category, in a way analogous to the dualitybetween (strongly) fp-injectivity and flatness in the module category.We shift our attention to Gorenstein homological Algebra. Projectively coresolved Gorenstein flat modules were introduced recently bySaroch and Stovicek and were shown to be Gorenstein projective. While therelation between Gorenstein projective and Gorenstein flat modules is notwell understood, the class of projectively coresolved Gorenstein flat modules iscontained in the class of Gorenstein flat modules. In this thesis necessaryand sufficient conditions for a module of finite Gorenstein flat dimension tobe projectively coresolved Gorenstein flat, or of finite flat dimension are proved.
Main subject category:
Science
Keywords:
K-Absolutely pure complexes, Strongly fp-injective modules, Gorenstein Homological Algebra, Homotopy category, Cotorsion pairs, Bousfield localizing pairs, Stable categories, Derived category
