Equivariant vector bundles on the Lubin - Tate moduli space

We discuss the first author's Picard groups of stable homo-topy. We give s. detailed description of the calculation of PiC!, and go onto describe geometric constructions for lifts of the elements of Pic!. Wealso construct a 15 cell complex that localizeil to what we speculate is aninteresting element ofPk2 •For all n we describe an algebraic approxllna-tion to Picn using the Adams-Novikov spectral sequence. We also showthat the p-wc integers embed in the group Pie" for all n and p. DEPARTMENT OF MATHEMATICS, HARVARD UNIVERSITY, CAMBRIDGE, MA