K₂ of families of elliptic curves over non-Abelian cubic and quartic fields

2024/01/09 by Brunault, François, de Jeu, Rob, Liu, Hang +1
#11G40 (secondary) #19E08 #19F27 (primary) #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.04510

Abstract

We give two constructions of families of elliptic curves over cubic or quartic fields with three, respectively four, `integral' elements in the kernel of the tame symbol on the curves. The fields are in general non-Abelian, and the elements linearly independent. For their integrality, we prove a new criterion that does not ignore any torsion. We also verify Beilinson's conjecture numerically for just over 90 of the curves.

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