A K-theoretic approach to Artin maps

2017/03/22 by Dustin Clausen, Clausen, Dustin · 1 voice · 1 citation
#math.KT #math.NT

paper · pdf · doi:10.48550/arxiv.1703.07842

Abstract

We define a functorial "Artin map" attached to any small \bfZ-linear stable ∞-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.

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Discussions

• What a wild theorem (Clausen, 2017): In a derived sense, second countable locally compact Hausdorff Abelian groups measure the difference between free Abelian groups and real vector spaces! arxiv.org/ [bsky, 8 points, 2 comments]

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