Orthogonal to principal ideles

TL;DR

This paper characterizes the orthogonal complement of principal ideles within the idele group using the global tame symbol pairing, advancing understanding of algebraic curves and their idele class groups.

Contribution

It provides a new description of the orthogonal to principal ideles with respect to the tame symbol pairing on algebraic curves.

Findings

Identifies the orthogonal complement of principal ideles.

Uses the global tame symbol pairing for characterization.

Enhances understanding of idele class groups in algebraic geometry.

Abstract

We describe the orthogonal to the group of principal ideles with respect to the global tame symbol pairing on the group of ideles of a smooth projective algebraic curve over a field.