This US-Brazil Cooperative Science award will support the research collaboration of Edward Green of Virginia Polytechnic Institute and State University and Eduardo Marcos of the University of Sao Paulo, Brazil. The project aims to explore the category of graded modules of a graded ring by studying the local theory which the two researchers have introduced. The PIs will investigate two specific problems. First, they will study finite dimensional algebras which are locally of finite type (a notion they have defined for graded algebras). They expect that these graded algebras should have the property that the number of "gradable" components in the Auslander-Reiten quiver is finite. Second, they will investigate the local structure of the category of graded Cohen-Macaulay modules over a graded local commutative algebra by studying an equivalent subcategory of the category of modules over a finite dimensional algebra. The US side will contribute expertise in graded modules and finite dimensional representation theory. The Brazilian side will contribute expertise in Cohen-Macaulay modules. Through this collaboration, both sides will gain a better understanding of representation theory, an important topic in mathematics.
