On K_2 of certain families of curves

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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 nonhyperelliptic curves of all composite genera g with g independent integral elements in the kernel of the tame symbol. We also give families of elliptic curves over real quadratic fields with two independent integral elements.
Original languageEnglish
Pages (from-to)10929-10958
Number of pages30
JournalInternational Mathematics Research Notices
Volume2015
Issue number21
Early online date2 Feb 2015
DOIs
Publication statusPublished - 2015

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