Galois theory and integral models of Λ-rings

Abstract

We show that any Λ-ring, in the sense of Riemann-Roch theory, which is finite etale over the rational numbers and has an integral model as a Λ-ring is contained in a product of cyclotomic fields. In fact, we show that the category of such Λ-rings is described in a Galois-theoretic way in terms of the monoid of pro-finite integers under multiplication and the cyclotomic character. We also study the maximality of these integral models and give a more precise, integral version of the result above. These results reveal an interesting relation between Λ-rings and the class field theory.