A K-theoretic approach to Artin maps

Abstract

We define a functorial "Artin map" attached to any small $\mathbf{Z}$-linear stable $\infty$-category, which in the case of perfect complexes over a global field recovers the usual Artin map from the idele class group to the abelianized absolute Galois group. In particular, this gives a new proof of the Artin reciprocity law.