A K-theoretic approach to Artin maps
Abstract
We define a functorial "Artin map" attached to any small $\bf{Z}$-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.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2017
- DOI:
- 10.48550/arXiv.1703.07842
- arXiv:
- arXiv:1703.07842
- Bibcode:
- 2017arXiv170307842C
- Keywords:
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- Mathematics - K-Theory and Homology;
- Mathematics - Number Theory