The celebrated Beilinson's conjecture establishes very far reaching relations
between algebraic K-theory and L-function of projective algebraic variety. In
the case of K_2 of algebraic curves over Q, Beilinson's conjecture on one hand
predicts the rank of the integral K2 group of algebraic curves equals the genus
g, on the other hand predicts the special value of the L-function L(C; 2) equals
the regulator multiplied by some simple factors and a non-zero rational number.
In this talk, 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. Thus the lower bound of the
rank of K_2 of these curves is the same as predicted by Beilinson's conjecture.

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