Beilinson-Kato elements in K_2 of modular curves
Résumé
This article investigates explicit linear dependence relations in the K_2-group of modular curves. In particular, it is shown that the Beilinson-Kato elements in K_2 of the modular curve Y(N) satisfy the Manin relations when N is not divisible by 3. Similar results are obtained for the modular curves X_1(N) and X_0(N) when N is prime. Finally we exhibit explicit generators of K_2, assuming the Beilinson conjecture.