An overview of abelian varieties in homotopy theory

Abstract

Through an investigation of properties of Chern classes, Quillen discovered a connection between stable homotopy theory and 1-dimensional formal group laws [41]. After almost 40 years, the impacts of this connection are still being felt. The stratification of formal group laws in finite characteristic gives rise to the chromatic filtration in stable homotopy theory [42], and has definite calculational consequences. The nilpotence and periodicity phenomena in stable homotopy groups of spheres arise from a deep investigation of this connection [13].