2020/08/13 by Rahul Gupta, Gupta, Rahul, Amalendu Krishna +1 · 1 citation
Mathematics · Psychology · #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Artificial intelligence #Class (philosophy) #Computer science #FOS: Mathematics #Fundamental group #Geometric and Algebraic Topology #Geometry #Group (periodic table) #Homomorphism #Interpretation (philosophy) #Mathematics #Modulus #Physics #Primary 14C25 #Psychology #Pure mathematics #Reciprocity (cultural anthropology) #Secondary 14F42 #Social psychology #math.AG #msc:14C25 #msc:14F42 #msc:19E15
paper · pdf · doi:10.48550/arxiv.2008.05719
published in arXiv (Cornell University) (Cornell University) · 50 pages. Final version, to appear in Journal of Algebra
openalex publication_date 2020/08/13 · arxiv created 2022/06/10 · arxiv updated 2022/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.