K2 of Elliptic Curves over Non-Abelian Cubic and Quartic Fields

Explore the intricacies of K_2 of elliptic curves over non-Abelian cubic and quartic fields in this 59-minute lecture by Rob de Jeu from the Hausdorff Center for Mathematics. Begin with a review of earlier results on K_2 of curves before delving into constructions of elliptic curve families over specific cubic or quartic fields. Examine the presence of three or four integral elements in the kernel of the tame symbol on these curves, noting that the fields are generally non-Abelian and the elements are linearly independent. Investigate a new criterion for integrality that accounts for all torsion. Conclude with a discussion on the numerical verification of Beilinson's conjecture for select curves, highlighting the collaborative nature of this work with François Brunault, Liu Hang, and Fernando Rodriguez Villegas.