9802852 Mitchell This project addresses problems in three distinct but closely related areas of homotopy theory: (1) homotopy fixed point spectra arising from the action of closed subgroups of the Morava stabilizer group on the Landweber exact spectrum whose coefficient ring is the functions on the Lubin-Tate moduli space of lifts (Devinatz); (2) multiplicative stable homotopy theory, the homotopy theory of operads, Andre-Quillen homology of algebras over simplicial operads (Goerss); and (3) etale homotopy type of rings of algebraic integers, with a view to applications in Iwasawa theory and algebraic K-theory (Mitchell). The broader goal of the project is to further our understanding of homotopy theory, the branch of topology concerned with those properties of higher-dimensional surfaces and other geometric objects that remain invariant under deformation. There are some surprising and rather mysterious connections between homotopy theory and seemingly unrelated fields such as number theory and algebraic geometry, and it is these connections that the investigators hope to elucidate. ***
