Article

# Galois theory and integral models of Lambda-rings

02/2008;
Source: arXiv

ABSTRACT We show that any Lambda-ring, in the sense of Riemann-Roch theory, which is finite etale over the rational numbers and has an integral model as a Lambda-ring is contained in a product of cyclotomic fields. In fact, we show that the category of them 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 Lambda-rings and class field theory.

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### Keywords

class field theory

cyclotomic character

cyclotomic fields

finite etale

Galois-theoretic way

integral models

integral version

interesting relation

Lambda-ring

Lambda-rings

maximality

pro-finite integers

Riemann-Roch theory