9402015 Murthy The principal investigator will study the structure of projective modules and efficient generation of modules over affine algebras. He will continue his work on finding obstructions to splitting of projective modules and efficient generation of ideals, analogous to obstruction theory for sections of vector bundles in topology. Some of the ingredients for these obstructions are Chow groups. Other invariants have to be explored. The tools used are from intersection theory, algebraic K-theory, and standard commutative algebra. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.
