  We construct a natural transformation from the Bousfield-Kuhn functor
evaluated on a space to the Topological Andre-Quillen cohomology of the
K(n)-local Spanier-Whitehead dual of the space, and show that the map is an
equivalence in the case where the space is a sphere. This results in a method
for computing unstable v_n-periodic homotopy groups of spheres from their
Morava E-cohomology (as modules over the Dyer-Lashof algebra of Morava
E-theory). We relate the resulting algebraic computations to the algebraic
geometry of isogenies between Lubin-Tate formal groups.
