Seminar

School of Mathematical Sciences, BNUAlgebra Seminar

题目:	Kaplansky classes and cotorsion theories.
报告人:	Dr. Javad Asadollahi (Institute for Research in Fundamental Science (IPM), Iran)
时间:	Friday, Mar. 23, 2012, 14:30 - 16:00
地点:	New Main Building, Room 1129
摘要:	Kaplansky classes were introduced by Enochs and Lopez-Romas. They used this notion to construct some complete cotorsion theories. Using this they get some precovering as well as enveloping classes of modules. In this lecture, we provide an argument that allow us to construct Kaplansky classes in the category of complexes starting from Kaplansky classes of modules. Our method while provide some new cotorsion theories in the category of complexes will recover most of the existing cotorsion theories.

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北师大表示论及相关课题研究群体 Mar. 14, 2012

Other information:

Dr. Javad Asadollahi from the University of Isfahan, Iran, will give a talk on "Tate Cohomology theory and its applications" at the Teaching Building No.2, Room 210, the Capital Normal University on March 28, 2012, Wednesday 14:30-16:00.
Abstract: Tate cohomology theory was initiated by Tate's observation, that the ZG-module Z with the trivial action, when G is a finite group, admits a complete projective resolution. Farrell generalized the theory to groups of finite virtual cohomological dimension. Mislin, Benson and Carlson and Vogel, independently, generalized the theory to all groups. Then it was shown that these theories are isomorphic, and complete cohomology is a common name for them. The theory has been studied also in the context of modules over rings. Auslander and Buchweitz studied maximal Cohen-CMacaulay modules over Gorenstein rings. This class of modules is a special case of modules in Auslander’s G-class, introduced by Auslander and developed by Auslander and Bridger. Using this class, Buchweitz studied Tate’s theory for finitely generated modules over Gorenstein rings. Enochs and collaborators generalized the theory to all modules. Avramov and Martsinkovsky, Asadollahi and Salarian, Krause, Jorgensen and Veliche also studied Tate cohomology theory in different settings. In this lecture, we will review the theory and will present some recent developments in the pure derived category of flats. This in particular, show that these theories can be extended naturally to sheaves over semi-separated noetherian schemes, where there are not always enough projectives, but we do have enough flats.