A geometric approach to the Cohen-Lenstra heuristics

2021/06/18 by Landesman, Aaron
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2106.10357

Abstract

We give a new geometric description of when an element of the class group of a quadratic field, thought of as a quadratic form q, is n-torsion. We show that q corresponds to an n-torsion element if and only if there exists a degree n polynomial whose resultant with q is ± 1. This is motivated by a more precise geometric parameterization which directly connects torsion in class groups of quadratic fields to Selmer groups of singular genus 1 curves.

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