Functorial Philosophy for Formal Phenomena
Neil Strickland
The purpose of this paper is to introduce the ``schematic viewpoint''
in algebraic topology. This seems to be the most natural framework in
which to discuss the algebraic structures which arise from
complex-oriented cohomology theories. Many of the parts which are
original are joint work with Mike Hopkins and Matthew Ando.
We give a definition of (formal) schemes which is well adapted to the
particular technicalities which arise in the study of Morava K-theory
and completed E(n)-theory. We show how to interpret the generalised
(co)homology of $CP^\infty$, $Z\times BU$, $B\Sigma_{p^m}$, projective
bundles and Thom spaces of complex vector bundles, and various other
spaces, using the language of formal group theory.