String bordism and chromatic characteristics

Abstract

We introduce characteristics into chromatic homotopy theory. This parallels the prime characteristics in number theory as well as in our earlier work on structured ring spectra and unoriented bordism theory. Here, the K(n)–local Hopkins–Miller classes ζn take the place of the prime numbers. Examples from topological and algebraic K-theory, topological modular forms, and higher bordism spectra motivate and illustrate this concept.