ABSTRACT:  Let R be the quotient of a regular coherent commutative ring by a finitely generated ideal. In this paper, we classify all abelian subcategories of finitely presented R-modules that are closed under extensions. In particular, when R is Noetherian, we find that every abelian subcategory of finitely generated modules is in fact a Serre subcategory.  We also classify abelian subcategories of arbitrary R-modules that are closed under extensions and coproducts, when R is
commutative and Noetherian.  The method relies on comparison with the derived category of R.
 
 

For further information visit the Seminar web page at http://www.northeastern.edu/martsinkovsky/p/rtrt.html  or contact Alex Martsinkovsky <alexmart@neu.edu>