TL;DR
This paper introduces a new notion of idele class groups for finitely generated fields using Parshin chains, providing an idelic perspective on higher class field theory as developed by Kato and Saito.
Contribution
It defines a novel idele class group framework for higher-dimensional fields, extending classical class field theory concepts.
Findings
Provides an idelic interpretation of higher class field theory
Defines idele class groups using Parshin chains for finitely generated fields
Bridges classical and higher-dimensional class field theories
Abstract
We propose a notion of idele class groups of finitely generated fields using the concept of Parshin chains. This new class group allows us to give an idelic interpretation of the higher class field theory of Kato and Saito.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry