Relative p-class groups and p-Selmer groups

2024/12/17 by Debajyoti De, De, Debajyoti, Dipramit Majumdar +3 · 1 citation
Mathematics · #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.2412.13022

Abstract

Let E be an elliptic curve with j-invariant 0 or 1728 and let \widetildeE be a k^th twist of E. We show that for any prime p of good reduction of \widetildeE, a degree k relative p-class group and the root number of \widetildeE determines the dimension of the p-Selmer group of \widetildeE. As a consequence, we construct families of large rank p-class group. We also relate congruent number and cube sum problem with relative p-class group.

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• On certain root number 1 cases of the cube sum problem

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