Selmer Groups and Quadratic Reciprocity

TL;DR

This paper investigates the structure of 2-Selmer groups in number fields and explores their relationship with quadratic reciprocity laws, providing new insights into algebraic number theory.

Contribution

It introduces novel connections between 2-Selmer groups and quadratic reciprocity in number fields, advancing understanding of their interplay.

Findings

Established links between 2-Selmer groups and quadratic reciprocity laws.

Provided new methods to analyze Selmer groups in number fields.

Enhanced comprehension of the algebraic structures underlying quadratic reciprocity.

Abstract

In this article we study the 2-Selmer groups of number fields $F$ as well as some related groups, and present connections to the quadratic reciprocity law in $F$.