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arXiv · 2008.05719

Reciprocity for Kato-Saito idele class group with modulus

Rahul Gupta·Amalendu Krishna
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Abstract

We introduce an etale fundamental group with modulus and construct a reciprocity homomorphism from the Kato-Saito idele class group with modulus to this fundamental group. This is the K-theoretic analogue of the reciprocity for the cycle-theoretic idele class group with modulus due to Kerz-Saito, and plays a central role in showing the isomorphism between the two idele class groups. It also provides a new interpretation of the already known etale fundamental group with modulus due to Deligne and Laumon.

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Rahul Gupta, Amalendu Krishna. 2020-08-13. Reciprocity for Kato-Saito idele class group with modulus. https://arxiv.org/abs/2008.05719

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