English

Reciprocity for Kato-Saito idele class group with modulus

Algebraic Geometry 2022-06-13 v4

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.

Cite

@article{arxiv.2008.05719,
  title  = {Reciprocity for Kato-Saito idele class group with modulus},
  author = {Rahul Gupta and Amalendu Krishna},
  journal= {arXiv preprint arXiv:2008.05719},
  year   = {2022}
}

Comments

50 pages. Final version, to appear in Journal of Algebra

R2 v1 2026-06-23T17:49:38.542Z