This project is concerned with several problems in commutative algera. The principal investigators will work on the Horrocks'conjecture. They will also work on the syzygy theorem and extending certain results to the mixed characteristic case. Another area of concentration concerns invariants related to representations of groups in positive characteristic. One of the main problems to be considered in this area is to describe how tensor functors, acting on indecomposable representations, decompose. The research in this project involves two areas of commutative algebra. The first area is concerned with the structure and properties of syzygies of finite projective dimension and uses local commutative algebra. A "syzygy" is a linking or yoking together of steps in a projective resolution describing the structure of a module. The second area is concerned with decomposing tensor functors under formal group laws and the properties of the relative Grothendieck groups that are associated to the decomposition.
