Orientations and p-Adic Analysis

Barry John Walker

Published 2009-04-30, updated 2009-05-04Version 2

Matthew Ando produced power operations in the Lubin-Tate cohomology theories and was able to classify which complex orientations were compatible with these operations. The methods used by Ando, Hopkins and Rezk to classify orientations of topological modular forms can be applied to complex K-Theory. Using techniques from local analytic number theory, we construct a theory of integration on formal groups of finite height. This calculational device allows us to show the equivalence of the two descriptions for complex K-Theory. As an application we show that the $p$-completion of the Todd genus is an $E_\infty$ map.