On K₂ of certain families of curves

2014/02/19 by Liu, Hang, de Jeu, Rob
#11G30 (Secondary) #19E08 #19F27 (Primary) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1402.4822

Abstract

We construct families of smooth, proper, algebraic curves in characteristic 0, of arbitrary genus g, together with g elements in the kernel of the tame symbol. We show that those elements are in general independent by a limit calculation of the regulator. Working over a number field, we show that in some of those families the elements are integral. We determine when those curves are hyperelliptic, finding, in particular, that over any number field we have non-hyperelliptic curves of all composite genera g with g independent integral elements in the kernel of the tame symbol.

Related

• K₂ of families of elliptic curves over non-Abelian cubic and quartic fields
• Bounding generators for the kernel and cokernel of the tame symbol for curves
• The a-number of hyperelliptic curves
• Rational and isolated quadratic points on hyperelliptic curves of rank 0 and small genus
• The Integral Chow Ring of the Stack of Pointed Hyperelliptic Curves