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Tame class field theory over local fields

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KA2W02 - Arithmetic geometry, cycles, Hodge theory, regulators, periods and heights

In this joint work with Rahul Gupta and Jitendra Rathore, we study the tame class field theory of smooth varieties over local fields. We construct a reciprocity homomorphism from the idele class group of a smooth variety $X$ over a local field $k$  to its abelian etale fundamental group. We describe the kernel and image of this reciprocity homomorphism away from the residue characteristic of  $k$. This generalizes the unramified class field theory over local fields due to Jannsen-Saito and Forre.

This talk is part of the Isaac Newton Institute Seminar Series series.

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