Depth Properties of Modules Over Local Rings

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WIEGAND98-01309This award supports research in homological and commutative algebra. Three related topics will be investigated: homological theory of local rings, representation theory of modules over local tings and Picard groups of algebraic varieties over field that are not algebraically closed.Commutative algebra, among other things, studies the solutions of polynomial or power series equations by forming an algebraic object, called a ring, which consists of the 'generic' solutions. The algebraic properties of these generic solutions then give insight into the geometric and algebraic nature of the equations. The field combines techniques from a number of other areas including combinatorics, topology, and analysis.