Abstract

The celebrated Beilinson's conjecture establishes very far reaching relations between algebraic K-theory and L-function of projective algebraic variety which generalizes and unifies multiple theorems and conjectures in number theory, e.g. the class number formula. In the case of K2 of algebraic curves over Q, Beilinson's conjecture on one hand gives the rank of the integral K2 group of algebraic curves, on the other hand predicts the relation between special value of the L-function L(C; 2) and regulator of K2.

In this talk, we first briefly review the background of K2 of curves. Then we will study K2 of certain families of curves of arbitrary genus and K2 of elliptic curves over nonabelian cubic and quartic fields.