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arXiv · 2401.04510

$K_2$ of families of elliptic curves over non-Abelian cubic and quartic fields

François Brunault·Rob de Jeu·Hang Liu·Fernando Rodriguez Villegas
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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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François Brunault, Rob de Jeu, Hang Liu, Fernando Rodriguez Villegas. 2024-01-09. $K_2$ of families of elliptic curves over non-Abelian cubic and quartic fields. https://arxiv.org/abs/2401.04510

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