WIEGAND, DMS-9709757 ABSTRACT Topics in Commutative Algebra and Algebraic Geometry This project will be undertaken by the research group in commutative algebra and algebraic geometry at the University of Nebraska--Lincoln. Roger Wiegand and Sylvia Wiegand will study local rings of finite Cohen-Macaulay type. R. Wiegand and Tom Marley will consider homological questions in the theory of local rings. S. Wiegand will study prime ideal structure in Noetherian rings and intermediate rings between a local ring and its completion. Brian Harbourne will investigate resolutions of ideals corresponding to finite sets of points (with multiplicities) in projective space. David Jaffe will study binary linear codes and their connections with the geometry of projective space. Judy Walker will work on coding theory, particularly over commutative Artinian rings. Mark Walker will investigate connections between algebraic I-theory and motivic cohomology. These investigations concern central problems in commutative algebra and algebraic geometry, and many of them are continuations of successful collaborations with researchers at other institutions. This project will allow the research group to continue its active involvement in collaborative research and to maintain its position as a leading research group in commutative algebra and algebraic geometry.
